Thursday, October 23, 2025

One Proportion vs Two Proportion Tests



## **One Proportion Test**


**Tests:** One sample proportion against a known/hypothesized population proportion


### **When to Use:**

- Comparing **one group** to a known standard or benchmark

- Testing if a **single proportion** differs from an expected value


### **Formula:**

```python

z = (p̂ - p₀) / √[p₀(1-p₀)/n]

```

Where:

- p̂ = sample proportion

- p₀ = hypothesized population proportion

- n = sample size


## **Two Proportion Test**


**Tests:** Difference between proportions from two independent groups


### **When to Use:**

- Comparing **two different groups** to each other

- Testing if proportions differ between two populations


### **Formula:**

```python

z = (p̂₁ - p̂₂) / √[p̂_pool(1-p̂_pool)(1/n₁ + 1/n₂)]

```

Where:

- p̂_pool = (x₁ + x₂)/(n₁ + n₂)


---


## **Decision Guide:**


```python

def choose_test():

    """Simple decision guide"""

    print("ASK YOURSELF: How many groups am I comparing?")

    print()

    print("šŸ” ONE PROPORTION TEST:")

    print("   Q: Is my SINGLE group different from a known standard?")

    print("   → Use when: Comparing to historical data/benchmark")

    print()

    print("šŸ” TWO PROPORTION TEST:") 

    print("   Q: Are these TWO GROUPS different from each other?")

    print("   → Use when: Comparing Group A vs Group B")

    

choose_test()

```


---


## **Real-World Examples:**


### **Example 1: One Proportion Test**

```python

# Scenario: Company Quality Claim

# "We deliver 95% of packages on time"

# Sample: 180 out of 200 packages delivered on time


# Question: "Does our actual performance match the 95% claim?"

# → ONE PROPORTION TEST (one group vs known standard)


from statsmodels.stats.proportion import proportions_ztest


# One proportion test

z_stat, p_value = proportions_ztest(count=180, nobs=200, value=0.95, alternative='two-sided')

print(f"One Proportion Test: z={z_stat:.3f}, p={p_value:.4f}")

```


### **Example 2: Two Proportion Test**

```python

# Scenario: Drug Effectiveness

# Drug A: 45 successes out of 50 patients

# Drug B: 35 successes out of 50 patients


# Question: "Is Drug A more effective than Drug B?"

# → TWO PROPORTION TEST (comparing two groups)


z_stat, p_value = proportions_ztest(count=[45, 35], nobs=[50, 50], value=0, alternative='larger')

print(f"Two Proportion Test: z={z_stat:.3f}, p={p_value:.4f}")

```


---


## **Detailed Comparison Table:**


| Aspect | One Proportion Test | Two Proportion Test |

|--------|---------------------|---------------------|

| **Groups Compared** | One sample vs known value | Two independent samples |

| **Research Question** | "Does our rate equal X%?" | "Are these two rates different?" |

| **Null Hypothesis** | H₀: p = p₀ | H₀: p₁ = p₂ |

| **Data Required** | p̂, n, p₀ | p̂₁, n₁, p̂₂, n₂ |

| **Common Use Cases** | Quality control, claim verification | A/B testing, treatment comparisons |


---


## **Medical Examples:**


### **One Proportion (Medical):**

```python

# Hospital Infection Rates

# National standard: Infection rate should be ≤ 2%

# Our hospital: 8 infections in 300 patients (2.67%)


# Question: "Does our hospital meet the national standard?"

# → ONE PROPORTION TEST


print("ONE PROPORTION TEST - Hospital Quality")

print("H₀: Our infection rate ≤ 2% (meets standard)")

print("H₁: Our infection rate > 2% (exceeds standard)")


z_stat, p_value = proportions_ztest(count=8, nobs=300, value=0.02, alternative='larger')

```


### **Two Proportion (Medical):**

```python

# Smoking by Gender

# Males: 40 smokers out of 150

# Females: 20 smokers out of 100


# Question: "Do smoking rates differ by gender?"

# → TWO PROPORTION TEST


print("TWO PROPORTION TEST - Smoking by Gender")

print("H₀: p_male = p_female (no difference)")

print("H₁: p_male ≠ p_female (rates differ)")


z_stat, p_value = proportions_ztest(count=[40, 20], nobs=[150, 100], value=0, alternative='two-sided')

```


---


## **Business Examples:**


### **One Proportion (Business):**

```python

# E-commerce Conversion Rate

# Industry benchmark: 3% conversion rate

# Our site: 45 conversions from 1200 visitors (3.75%)


# Question: "Is our conversion rate better than industry average?"

# → ONE PROPORTION TEST


z_stat, p_value = proportions_ztest(count=45, nobs=1200, value=0.03, alternative='larger')

```


### **Two Proportion (Business):**

```python

# Marketing Campaign A/B Test

# Version A: 120 clicks from 2000 impressions (6%)

# Version B: 90 clicks from 2000 impressions (4.5%)


# Question: "Which ad version performs better?"

# → TWO PROPORTION TEST


z_stat, p_value = proportions_ztest(count=[120, 90], nobs=[2000, 2000], value=0, alternative='larger')

```


---


## **Key Questions to Determine Which Test:**


### **Ask These Questions:**


#### **For One Proportion Test:**

1. "Am I comparing **one group** to a **known standard**?"

2. "Do I have a **historical benchmark** to compare against?"

3. "Is there a **target value** I'm trying to achieve?"

4. "Am I testing a **claim** about a single population?"


#### **For Two Proportion Test:**

1. "Am I comparing **two different groups**?"

2. "Do I want to know if **Group A differs from Group B**?"

3. "Am I running an **A/B test** or **treatment comparison**?"

4. "Are these **independent samples** from different populations?"


---


## **Complete Decision Framework:**


```python

def proportion_test_selector():

    """Interactive test selector"""

    

    print("PROPORTION TEST SELECTOR")

    print("=" * 40)

    

    questions = [

        "How many groups are you analyzing? (1/2)",

        "Do you have a known benchmark to compare against? (yes/no)", 

        "Are you comparing two different treatments/conditions? (yes/no)",

        "Is this quality control against a standard? (yes/no)",

        "Are you testing if two groups differ from each other? (yes/no)"

    ]

    

    print("\nAnswer these questions:")

    for i, question in enumerate(questions, 1):

        print(f"{i}. {question}")

    

    print("\nšŸŽÆ QUICK DECISION GUIDE:")

    print("• Known standard + One group → ONE PROPORTION TEST")

    print("• Two groups comparison → TWO PROPORTION TEST")

    print("• Quality control → ONE PROPORTION TEST") 

    print("• A/B testing → TWO PROPORTION TEST")


proportion_test_selector()

```


---


## **When to Use Each - Summary:**


### **✅ Use ONE PROPORTION TEST when:**

- Testing against **industry standards**

- **Quality control** checks

- Verifying **company claims**

- Comparing to **historical data**

- **Regulatory compliance** testing


### **✅ Use TWO PROPORTION TEST when:**

- **A/B testing** (website versions, ads, etc.)

- **Treatment comparisons** (drug A vs drug B)

- **Demographic comparisons** (male vs female, young vs old)

- **Geographic comparisons** (Region A vs Region B)

- **Time period comparisons** (before vs after campaign)


---


## **Statistical Note:**


```python

# Both tests rely on these assumptions:

assumptions = {

    'random_sampling': 'Data collected through random sampling',

    'independence': 'Observations are independent', 

    'sample_size': 'np ≥ 10 and n(1-p) ≥ 10 for each group',

    'normal_approximation': 'Sample size large enough for normal approximation'

}

```


## **Bottom Line:**


**Choose One Proportion Test when comparing to a known standard. Choose Two Proportion Test when comparing two groups to each other.**


The key distinction is whether you have an **external benchmark** (one proportion) or are making an **internal comparison** (two proportions)!

What is Open Semantic Interchange (OSI) initiative?

 The Open Semantic Interchange (OSI) initiative is a new, collaborative effort launched by companies like Snowflake, Salesforce, and dbt Labs to create a vendor-neutral, open standard for sharing semantic models across different AI and analytics tools. The goal is to solve the problem of fragmented data definitions and inconsistent business logic, which hinder data interoperability and make it difficult to trust AI-driven insights. By providing a common language for semantics, OSI aims to enhance interoperability, accelerate AI and BI adoption, and streamline operations for data teams. 

Key goals and features

Enhance interoperability: Create a shared semantic standard so that all AI, BI, and analytics tools can "speak the same language," allowing for greater flexibility in choosing best-of-breed technologies without sacrificing consistency. 

Accelerate AI and BI adoption: By ensuring semantic consistency across platforms, OSI builds trust in AI insights and makes it easier to scale AI and BI applications. 

Streamline operations: Eliminate the time data teams spend reconciling conflicting definitions or duplicating work by providing a common, open specification. 

Promote a model-first, metadata-driven architecture: OSI supports architectures where business meaning is defined in a central model, which can then be used consistently across various tools. 

Why it matters

Breaks down data silos: In today's complex data landscape, definitions are often scattered and inconsistent across different tools and platforms. OSI provides a universal way for these definitions to travel seamlessly between systems. 

Builds trust in AI: Fragmented semantics are a major roadblock to trusting AI-driven answers, as different tools may interpret the same business logic differently. A standard semantic layer ensures more accurate and trustworthy insights. 

Empowers organizations: A universal standard gives enterprises the freedom to adopt the best tools for their needs without worrying about semantic fragmentation, leading to greater agility and efficiency. 

What is Context Engineering?

“the art and science of filling the context window with just the right information at each step of an agent’s trajectory.” Lance Martin of LangChain

Lance Martin breaks down context engineering into four categories: write, compress, isolate, and select. Agents need to write (or persist or remember) information from task to task, just like humans. Agents will often have too much context as they go from task to task and need to compress or condense it somehow, usually through summarization or ‘pruning’. Rather than giving all of the context to the model, we can isolate it or split it across agents so they can, as Anthropic describes it, “explore different parts of the problem simultaneously”. Rather than risk context rot and degraded results, the idea here is to not give the LLM enough rope to hang itself. 


Context engineering needs a semantic layer

What is a Semantic Layer?

A semantic layer is a way of attaching metadata to all data in a form that is both human and machine readable, so that people and computers can consistently understand, retrieve, and reason over it.

There is a recent push from those in the relational data world to build a semantic layer over relational data. Snowflake even created an Open Semantic Interchange (OSI) initiative to attempt to standardize the way companies are documenting their data to make it ready for AI. 

VArious types of re-rankers

 a re-ranker is, after you bring the facts, how do you decide what to keep and what to throw away, [and that] has a big impact.” Popular re-rankers are 

Cohere Rerank, 

Voyage AI Rerank,

 Jina Reranker, and 

BGE Reranker. 

Re-ranking is not enough in today’s agentic world. The newest generation of RAG has become embedded into agents–something increasingly known as context engineering. 

Cohere Rerank, Voyage AI Rerank, Jina Reranker, and BGE Reranker are all models designed to improve the relevance of search results, particularly in Retrieval Augmented Generation (RAG) systems, by re-ordering a list of retrieved documents based on their semantic relevance to a given query. While their core function is similar, they differ in several key aspects:

1. Model Focus & Strengths:

Cohere Rerank: Known for its strong performance and general-purpose reranking capabilities across various data types (lexical, semantic, semi-structured, tabular). It also emphasizes multilingual support.

Voyage AI Rerank: Optimized for high-performance reranking, particularly in RAG and search applications. Recent versions (e.g., rerank-2.5) focus on instruction-following capabilities and improved context length.

Jina Reranker: Excels in multilingual support and offers high throughput, especially with its v2-base-multilingual model. It also supports agentic tasks and code retrieval.

BGE Reranker: Provides multilingual support and multi-functionality, including dense, sparse, and multi-vector (Colbert) retrieval. It can handle long input lengths (up to 8192 tokens). 

2. Performance & Accuracy:

Performance comparisons often show variations depending on the specific dataset and evaluation metrics. Voyage AI's rerank-2 and rerank-2-lite models, for instance, have shown improvements over Cohere v3 and BGE v2-m3 in certain benchmarks. Jina's multilingual model also highlights its strong performance in cross-lingual scenarios.

3. Features & Capabilities:

Multilingual Support: All models offer multilingual capabilities to varying degrees, with Jina and BGE specifically highlighting their strong multilingual performance.

Instruction Following: Voyage AI's rerank-2.5 and rerank-2.5-lite introduce instruction-following features, allowing users to guide the reranking process using natural language.

Context Length: BGE Reranker stands out with its ability to handle long input lengths (up to 8192 tokens). Voyage AI's newer models also offer increased context length.

Specific Use Cases: Jina emphasizes its suitability for agentic tasks and code retrieval, while Voyage AI focuses on RAG and general search.

4. Implementation & Accessibility:

Some rerankers are available as APIs, while others might offer open-source models for self-hosting. The ease of integration with existing systems (e.g., LangChain) can also be a differentiating factor.

5. Cost & Resources:

Model size and complexity directly impact computational cost and latency. Lighter models (e.g., Voyage AI rerank-2-lite) are designed for speed and efficiency, while larger models offer higher accuracy but demand more resources. Pricing models, such as token-based pricing, also vary between providers.

In summary, the choice of reranker depends on specific needs, including the required level of accuracy, multilingual support, context length, performance constraints, and integration preferences. Evaluating these factors against the strengths of each model is crucial for selecting the optimal solution.


What is Context Rot?

 Context rot is the degradation of an LLM's performance as the input or conversation history grows longer. It causes models to forget key information, become repetitive, or provide irrelevant or inaccurate answers, even on simple tasks, despite having a large context window. This happens because the model struggles to track relationships between all the "tokens" in a long input, leading to a decrease in performance. 

How context rot manifests

Hallucinations: The model may confidently state incorrect facts, even when the correct information is present in the prompt. 

Repetitive answers: The AI can get stuck in a loop, repeating earlier information or failing to incorporate new instructions. 

Losing focus: The model might fixate on minor details while missing the main point, resulting in generic or off-topic responses. 

Inaccurate recall: Simple tasks like recalling a name or counting can fail with long contexts. 

Why it's a problem

Diminishing returns: Even though models are built with large context windows, simply stuffing more information into them doesn't guarantee better performance and can actually hurt it. 

Impact on applications: This is a major concern for applications built on LLMs, as it can make them unreliable, especially in extended interactions like long coding sessions or conversations. 

How to mitigate context rot

Just-in-time retrieval: Instead of loading all data at once, use techniques that dynamically load only the most relevant information when it's needed. 

Targeted context: Be selective about what information is included in the prompt and remove unnecessary or stale data. 

Multi-agent systems: For complex tasks, consider breaking them down and using specialized sub-agents to avoid overwhelming a single context. 

What is DRIFT search

 However, we haven’t yet explored DRIFT search, which will be the focus of this blog post. DRIFT is a newer approach that combines characteristics of both global and local search methods. The technique begins by leveraging community information through vector search to establish a broad starting point for queries, then uses these community insights to refine the original question into detailed follow-up queries. This allows DRIFT to dynamically traverse the knowledge graph to retrieve specific information about entities, relationships, and other localized details, balancing computational efficiency with comprehensive answer quality


DRIFT search presents an interesting strategy for balancing the breadth of global search with the precision of local search. By starting with community-level context and progressively drilling down through iterative follow-up queries, it avoids the computational overhead of processing all community reports while still maintaining comprehensive coverage.

However, there’s room for several improvements. The current implementation treats all intermediate answers equally, but filtering based on their confidence scores could improve final answer quality and reduce noise. Similarly, follow-up queries could be ranked by relevance or potential information gain before execution, ensuring the most promising leads are pursued first.

Another promising enhancement would be introducing a query refinement step that uses an LLM to analyze all generated follow-up queries, grouping similar ones to avoid redundant searches and filtering out queries unlikely to yield useful information. This could significantly reduce the number of local searches while maintaining answer quality.


https://towardsdatascience.com/implementing-drift-search-with-neo4j-and-llamaindex/

https://towardsdatascience.com/implementing-drift-search-with-neo4j-and-llamaindex/

Sunday, October 19, 2025

Simple program for finding out the p-value for rejecting null hypothesis

 import numpy as np

import scipy.stats as stats


# energy expenditure (in mJ) and stature (0=obese, 1=lean)

energy = np.array([[9.21, 0],[7.53, 1],[7.48, 1],[8.08, 1],[8.09, 1],[10.15, 1],[8.40, 1],[0.88, 1],[1.13, 1],[2.90, 1],[11.51, 0],[2.79, 0],[7.05, 1],[1.85, 0],[19.97, 0],[7.48, 1],[8.79, 0],[9.69, 0],[2.68, 0],[3.58, 1],[9.19, 0],[4.11, 1]])


# Separating the data into 2 groups

group1 = energy[energy[:, 1] == 0] # elements of the array where obese == True

group1 = group1[:,0] # energy expenditure of obese

group2 = energy[energy[:, 1] == 1] # elements of the array where lean == True

group2 = group2[:,0] # energy expenditure of lean


# Perform t-test

t_statistic, p_value = stats.ttest_ind(group1, group2, equal_var=True)


print("T-TEST RESULTS: Obese (0) vs Lean (1) Energy Expenditure")

print("=" * 55)

print(f"Obese group (n={len(group1)}): Mean = {np.mean(group1):.2f} mJ, Std = {np.std(group1, ddof=1):.2f} mJ")

print(f"Lean group (n={len(group2)}): Mean = {np.mean(group2):.2f} mJ, Std = {np.std(group2, ddof=1):.2f} mJ")

print(f"\nT-statistic: {t_statistic:.4f}")

print(f"P-value: {p_value:.4f}")


# Interpretation

alpha = 0.05

print(f"\nINTERPRETATION (α = {alpha}):")

if p_value < alpha:

    print("✅ REJECT NULL HYPOTHESIS")

    print("   There is a statistically significant difference in energy expenditure")

    print("   between obese and lean individuals.")

else:

    print("❌ FAIL TO REJECT NULL HYPOTHESIS")

    print("   No statistically significant difference in energy expenditure")

    print("   between obese and lean individuals.")


# Show the actual data

print(f"\nOBESE GROUP ENERGY EXPENDITURE: {group1}")

print(f"LEAN GROUP ENERGY EXPENDITURE: {group2}")


Saturday, October 18, 2025

What is resource quota and what is Limit Range in Kubernetes ?

ResourceQuota = "Don't let this namespace use more than X total resources"

LimitRange = "Each container in this namespace should have resources between Y and Z"

They work together to provide both macro-level (namespace) and micro-level (container) resource management in your Kubernetes cluster.



ResourceQuota vs LimitRange - Key Differences

Aspect ResourceQuota LimitRange

Purpose Enforces total resource limits for a namespace Sets defaults and constraints for individual containers

Scope Namespace-level (affects all resources in namespace) Container/Pod-level (affects individual containers)

What it controls Aggregate resource consumption across all pods Resource requests/limits per container

Enforcement Prevents namespace from exceeding total quota Validates individual pod spe


spec:

  hard:

    requests.cpu: "1"           # Total CPU requests in namespace ≤ 1 core

    requests.memory: 1Gi        # Total memory requests in namespace ≤ 1GB

    limits.cpu: "2"             # Total CPU limits in namespace ≤ 2 cores  

    limits.memory: 2Gi          # Total memory limits in namespace ≤ 2GB

    pods: "10"                  # Max 10 pods in namespace

    services: "5"               # Max 5 services in namespace

    secrets: "10"               # Max 10 secrets in namespace

    configmaps: "10"            # Max 10 configmaps in namespace

    persistentvolumeclaims: "5" # Max 5 PVCs in namespace



spec:

  limits:

  - default:                    # Applied when no limits specified

      cpu: 500m                # Default CPU limit = 0.5 cores

      memory: 512Mi            # Default memory limit = 512MB

    defaultRequest:            # Applied when no requests specified  

      cpu: 100m                # Default CPU request = 0.1 cores

      memory: 128Mi            # Default memory request = 128MB

    type: Container



Practical Examples

Scenario 1: Pod without resource specifications



apiVersion: 1.0

kind: pod

metadata:

   name: test-pod

   namespace: dev

spec:

   Containers:

   - name: app 

     image:nginx 

     # no resources specified 


Below is what happens 


LimitRange applies defaults: 

 requests.cpu 100m, requests.memory: 128mi 

 limits.cpu : 500m, limits.memory: 512Mi 


ResourceQuota counts these toward namespace totals


Scenario 2: Multiple pods and quota enforcement

Let's see how they work together:


# Check current usage

kubectl describe resourcequota dev-quota -n dev


Name:            dev-quota

Namespace:       dev

Resource         Used   Hard

--------         ----   ----

limits.cpu       500m   2

limits.memory    512Mi  2Gi

requests.cpu     100m   1

requests.memory  128Mi  1Gi

pods             1      10



Real-world Interaction Examples


Example 1: Pod creation within limits



apiVersion: v1

kind: Pod

metadata:

  name: pod-1

  namespace: dev

spec:

  containers:

  - name: app

    image: nginx

    resources:

      requests:

        cpu: 200m

        memory: 256Mi

      limits:

        cpu: 400m

        memory: 512Mi

 LimitRange: No validation issues (with



LimitRange: No validation issues (within min/max bounds)

ResourceQuota: Sufficient quota remaining



Example 2: Pod creation exceeding quota


apiVersion: v1

kind: Pod

metadata:

  name: pod-large

  namespace: dev

spec:

  containers:

  - name: app

    image: nginx

    resources:

      requests:

        cpu: 2    # 2 cores

        memory: 2Gi

      limits:

        cpu: 4    # 4 cores  

        memory: 4Gi



Example 3: Too many pods


After creating 10 pods, the 11th pod fails:


kubectl get pods -n dev

# Error: pods "pod-11" is forbidden: exceeded quota: dev-quota



Common Use Cases

ResourceQuota Use Cases:

Multi-tenant clusters - Prevent one team from consuming all resources


Cost control - Limit resource consumption per project/environment


Resource isolation - Ensure fair sharing of cluster resources


LimitRange Use Cases:

Prevent resource hogging - Set maximum limits per container


Ensure quality of service - Set minimum guarantees per container


Developer convenience - Provide sensible defaults


Resource validation - Catch misconfigured pods early




Advanced LimitRange Features

You can enhance your LimitRange with more constraints:


apiVersion: v1

kind: LimitRange

metadata:

  name: advanced-limits

  namespace: dev

spec:

  limits:

  - type: Container

    max:

      cpu: "1"

      memory: "1Gi"

    min:

      cpu: "10m" 

      memory: "4Mi"

    default:

      cpu: "500m"

      memory: "512Mi"

    defaultRequest:

      cpu: "100m"

      memory: "128Mi"

  - type: Pod

    max:

      cpu: "2"

      memory: "2Gi"



# Check quota usage

kubectl describe resourcequota dev-quota -n dev


# Check limit ranges

kubectl describe limitrange dev-limits -n dev


# See what defaults are applied to a pod

kubectl get pod <pod-name> -n dev -o yaml


# Check if pods are failing due to quotas

kubectl get events -n dev --field-selector reason=FailedCreate

What is two tailed Hypothesis test. When it is used

   

## Explanation:


In a **two-tailed hypothesis test**, the rejection region is **split between both tails** of the distribution.


## Visual Representation:


```

Two-Tailed Test (α = 0.05)

Rejection Region: Both tails (2.5% in each tail)


         │

    ┌────┼────┐

    │    │    │

    │    │    │

    │    │    │

[####]   │   [####]   ← Rejection regions (2.5% each)

    │    │    │

    │    │    │

    │    │    │

-1.96   0   1.96     ← Critical values

```


## Mathematical Confirmation:


```python

from scipy import stats


# For α = 0.05 two-tailed test:

alpha = 0.05

critical_value = stats.norm.ppf(1 - alpha/2)  # 1.96


print(f"Two-tailed critical values: ±{critical_value:.3f}")

print(f"Rejection region: z < -{critical_value:.3f} OR z > {critical_value:.3f}")

print(f"Area in left tail: {alpha/2:.3f} ({alpha/2*100}%)")

print(f"Area in right tail: {alpha/2:.3f} ({alpha/2*100}%)")

```


**Output:**

```

Two-tailed critical values: ±1.960

Rejection region: z < -1.960 OR z > 1.960

Area in left tail: 0.025 (2.5%)

Area in right tail: 0.025 (2.5%)

```


## Why This is True:


### **Two-Tailed Test Logic:**

- **H₀:** μ = μ₀ (No difference)

- **H₁:** μ ≠ μ₀ (Difference in EITHER direction)

- We reject H₀ if the test statistic is **significantly large OR significantly small**

- Therefore, we need **rejection regions on both sides**


### **Comparison with One-Tailed Tests:**


| Test Type | Rejection Region | Hypothesis |

|-----------|------------------|------------|

| **Two-Tailed** | **Both tails** | H₁: μ ≠ μ₀ |

| **Right-Tailed** | Right tail only | H₁: μ > μ₀ |

| **Left-Tailed** | Left tail only | H₁: μ < μ₀ |


## Medical Example:


```python

# Testing if a drug changes blood pressure (could increase OR decrease)

# Two-tailed test is appropriate


print("Two-tailed test scenario:")

print("H₀: Drug has NO effect on blood pressure (μ = 120)")

print("H₁: Drug CHANGES blood pressure (μ ≠ 120)")

print("→ We reject if blood pressure is significantly HIGHER OR LOWER")

print("→ Therefore, rejection regions on BOTH sides")

```


## Key Point:


The statement **"In a two-tailed hypothesis test, the rejection region lies on both sides of the distribution"** is **definitely TRUE** and represents the fundamental characteristic that distinguishes two-tailed tests from one-tailed tests.


Monday, October 6, 2025

Various ways to reset the git credentials

 To checkout a branch with username in the URL so it prompts for credentials, you have several options:


## Method 1: Clone with Username and Checkout Branch


```bash

git clone -b branch-name https://username@wwwin-github.company.com/username/repository.git

```


Example:

```bash

git clone -b feature/new-feature https://john@wwwin-github.company.com/team/project.git

```


## Method 2: Clone First, Then Checkout Branch


```bash

# Clone with username (will prompt for credentials)

git clone https://username@wwwin-github.company.com/username/repository.git


# Then checkout the specific branch

cd repository

git checkout branch-name

```


## Method 3: If Repository Already Exists


If you already have the repository but need to update the remote URL:


```bash

# Update remote URL to include username

git remote set-url origin https://username@wwwin-github.company.com/username/repository.git


# Fetch and checkout branch (will prompt for credentials)

git fetch origin

git checkout branch-name

```


## Method 4: Using Full URL for Specific Branch


```bash

# One-liner to clone and checkout specific branch with username

git clone --branch branch-name https://username@wwwin-github.company.com/username/repository.git

```


## Method 5: For Existing Clone - Reset and Re-authenticate


If you're having credential issues with an existing clone:


```bash

# Reset credentials first

echo "url=https://wwwin-github.company.com" | git credential reject


# Update remote with username

git remote set-url origin https://username@wwwin-github.company.com/username/repository.git


# Now checkout branch (will prompt for credentials)

git checkout branch-name

git pull origin branch-name

```


## Step-by-Step Example:


```bash

# Step 1: Clone with username and specific branch

git clone -b development https://your-username@wwwin-github.company.com/team/project.git


# You'll be prompted:

# Password for 'https://your-username@wwwin-github.company.com': 


# Step 2: Verify

cd project

git branch  # Should show you're on 'development' branch

git log --oneline -5  # Should show recent commits

```


## If You Want to Switch Branches Later:


```bash

# This should prompt for credentials if not cached

git checkout another-branch

git pull origin another-branch

```


## For Personal Access Tokens:


If using GitHub personal access tokens:


```bash

git clone -b branch-name https://username:token@wwwin-github.company.com/username/repository.git

```


**Note:** Be careful with this method as it stores the token in git config.


## Verification:


After successful checkout:

```bash

git status

git branch --show-current  # Shows current branch name

git log --oneline -3  # Shows recent commits

```


## Most Common Approach:


```bash

# This will prompt for credentials and checkout the branch directly

git clone -b your-branch-name https://your-username@wwwin-github.company.com/username/repository.git

```


The `-b` flag tells Git to checkout that specific branch immediately after cloning, and including the username in the URL ensures Git knows which credentials to request.

What is Type 1 and Type 2 errors in Null Hypothesis

**Example of a Type 1 Error:**

---

### **Scenario: Medical Testing for a Disease**


- **Null Hypothesis (\(H_0\))**: The patient does **not** have the disease.

- **Alternative Hypothesis (\(H_a\))**: The patient **has** the disease.


---


### **What Happens in a Type 1 Error:**


1. **Reality**: The patient is actually **healthy** (null hypothesis is **true**).

2. **Test Result**: The diagnostic test incorrectly shows **positive** for the disease.

3. **Decision**: Doctor rejects the null hypothesis and concludes the patient **has** the disease.

4. **Outcome**: **False positive** – the patient is told they have a disease they don't actually have.


---


### **Consequences:**

- Unnecessary stress and anxiety for the patient

- Further invasive testing that wasn't needed

- Wasted medical resources

- Potential side effects from unnecessary treatment


---


### **Statistical Context:**

- **Significance level (α)**: The probability of making a Type 1 error

- If α = 0.05, there's a 5% chance of rejecting a true null hypothesis

- In our example: 5% chance of diagnosing a healthy person as sick


---


### **Other Real-World Examples:**


1. **Justice System**: Convicting an innocent person (null: defendant is innocent)

2. **Quality Control**: Rejecting a good batch of products (null: batch meets quality standards)

3. **Drug Testing**: Concluding a drug works when it doesn't (null: drug has no effect)


---


**Type 1 errors represent "false alarms" – we see an effect that isn't really there.**







 

Kubernetes - HPA autoscaler and replica set

 In the below diagram, does how does HPA manages the deployment? 



1. What HPA Does

The HPA watches the Deployment (or sometimes a StatefulSet, ReplicaSet, etc.) and:

Monitors metrics like CPU utilization, memory usage, or custom metrics.

Adjusts the .spec.replicas field in the Deployment automatically to keep those metrics within target thresholds.

2. How the Connection Works

Here’s the sequence:

You create a Deployment (e.g., dev-app) with an initial replica count (say 2).

You create an HPA resource that targets the Deployment by name:


apiVersion: autoscaling/v2

kind: HorizontalPodAutoscaler

metadata:

  name: dev-app-hpa

spec:

  scaleTargetRef:

    apiVersion: apps/v1

    kind: Deployment

    name: dev-app

  minReplicas: 2

  maxReplicas: 10

  metrics:

    - type: Resource

      resource:

        name: cpu

        target:

          type: Utilization

          averageUtilization: 60


The Kubernetes control plane (controller manager) continuously checks:

The current CPU usage of pods managed by dev-app.

If average CPU > 60%, the HPA increases .spec.replicas in the Deployment (e.g., from 2 → 4).

If usage drops, it scales down again (e.g., 4 → 2).

The Deployment controller then updates its ReplicaSet, which creates or deletes pods accordingly.


HPA does NOT deploy → Deployment

HPA monitors → Deployment’s metrics

HPA modifies → Deployment’s replica count

Deployment manages → ReplicaSet

ReplicaSet manages → Pods



Sunday, October 5, 2025

Statistics What is Null and Alternate Hypothesis?

In statistics, we often want to test a claim or theory about a population (e.g., "This new drug is effective," "Our new website design increases sales"). Since we can't test the entire population, we use sample data. The Null and Alternative Hypotheses are two competing, mutually exclusive statements about this population.

Of course. This is a fundamental concept in statistics used in hypothesis testing.

### The Core Idea

In statistics, we often want to test a claim or theory about a **population** (e.g., "This new drug is effective," "Our new website design increases sales"). Since we can't test the entire population, we use sample data. The **Null** and **Alternative Hypotheses** are two competing, mutually exclusive statements about this population.

---

### 1. The Null Hypothesis (\(H_0\))


*   **What it is:** The **default or status quo** assumption. It's a statement of "no effect," "no difference," or "no change." It represents skepticism.

*   **Symbol:** \(H_0\)

*   **It always contains an equality:** \(=\), \(\leq\), or \(\geq\).

*   **The goal of a hypothesis test is to gather evidence *against* the null hypothesis.**


    **Examples:**

    *   A new drug is no better than a placebo. (\(H_0: \mu_{\text{drug}} = \mu_{\text{placebo}}\))

    *   The mean height of men is 175 cm. (\(H_0: \mu = 175\))

    *   The proportion of defective items is less than or equal to 2%. (\(H_0: p \leq 0.02\))


Think of it like a courtroom principle: **The defendant is innocent until proven guilty.** The null hypothesis is the assumption of innocence.


---


### 2. The Alternative Hypothesis (\(H_1\) or \(H_a\))


*   **What it is:** The **researcher's claim** or what you hope to prove. It's a statement that contradicts the null hypothesis. It represents a new effect, difference, or change.

*   **Symbol:** \(H_1\) or \(H_a\)

*   **It never contains an equality:** \(\neq\), \(>\), or \(<\).

*   **We only accept the alternative hypothesis if the sample data provides strong enough evidence to *reject* the null hypothesis.**


    **Examples (corresponding to the nulls above):**

    *   The new drug is better than the placebo. (\(H_a: \mu_{\text{drug}} > \mu_{\text{placebo}}\))

    *   The mean height of men is not 175 cm. (\(H_a: \mu \neq 175\))

    *   The proportion of defective items is greater than 2%. (\(H_a: p > 0.02\))


In the courtroom analogy, this is the **prosecution's claim** that the defendant is guilty.


---


### How They Work Together


1.  **State the Hypotheses:** You define both \(H_0\) and \(H_a\) before collecting data.

2.  **Collect Sample Data:** You gather evidence from the real world.

3.  **Perform a Statistical Test:** This calculates a probability (p-value) of observing your sample data *if the null hypothesis were true*.

4.  **Make a Decision:**

    *   If the evidence is very unlikely under \(H_0\) (p-value is low), you **reject the null hypothesis** in favor of the alternative. This is like finding the defendant "guilty."

    *   If the evidence is not unlikely under \(H_0\) (p-value is high), you **fail to reject the null hypothesis.** This is like a verdict of "not guilty." (Note: We never "accept" the null; we just don't have enough evidence to reject it).


---


### Key Takeaway Table


| Feature | Null Hypothesis (\(H_0\)) | Alternative Hypothesis (\(H_a\)) |

| :--- | :--- | :--- |

| **Represents** | Status quo, no effect, no difference | Researcher's claim, an effect, a difference |

| **Symbol** | \(H_0\) | \(H_1\) or \(H_a\) |

| **Contains** | \(=\), \(\leq\), \(\geq\) | \(\neq\), \(>\), \(<\) |

| **Court Analogy** | Innocence | Guilt |

| **Goal of Test** | Gather evidence to **reject** it | Gather evidence to **support** it |


**Analogy Summary:** You assume the null hypothesis is true (like assuming innocence). The sample data is the evidence. If the evidence is strong enough against the null, you reject it and side with the alternative.


Statistics: Dissecting a confidence interval question

Suppose the question is like this below 

A random sample of 100 men is taken and their mean height is calculated to be 180 cm. The population variance is 36 cm2. Find the 95% confidence interval for the mean height of the population.

Let’s go step-by-step.

---


**Step 1: Identify given values**


- Sample size \( n = 100 \)

- Sample mean \( \bar{x} = 180 \) cm

- Population variance \( \sigma^2 = 36 \) cm² → Population standard deviation \( \sigma = \sqrt{36} = 6 \) cm

- Confidence level \( 95\% \)


---


**Step 2: Determine the formula for confidence interval**


For a population with known standard deviation \(\sigma\), the \( 95\% \) confidence interval for the population mean \(\mu\) is:


\[

\bar{x} \pm z_{\alpha/2} \cdot \frac{\sigma}{\sqrt{n}}

\]


For \( 95\% \) confidence, \( z_{\alpha/2} = 1.96 \).


---


**Step 3: Compute standard error**


\[

\text{Standard error} = \frac{\sigma}{\sqrt{n}} = \frac{6}{\sqrt{100}} = \frac{6}{10} = 0.6

\]


---


**Step 4: Compute margin of error**


\[

\text{Margin of error} = 1.96 \times 0.6 = 1.176

\]


---


**Step 5: Construct confidence interval**


\[

180 \pm 1.176

\]


\[

(180 - 1.176, \ 180 + 1.176)

\]

\[

(178.824, \ 181.176)

\]


---


**Final answer:**

\[

\boxed{(178.824, 181.176)}

\]


This means we are \( 95\% \) confident that the true population mean height lies between \( 178.824 \) cm and \( 181.176 \) cm.


Statistics: Sample mean, Population Mean and relationships

Of course. This is a fundamental concept in statistics. Let's break it down clearly.

### 1. What is the Population Mean?

*   **Definition:** The population mean (denoted by the Greek letter **μ**, "mu") is the **true average** of a specific characteristic for the **entire group** (the population) you are interested in.

*   **The Goal:** In statistics, the population mean is often the ultimate parameter we want to know but usually **cannot measure directly**.

    **Examples:**

    *   If your population is "all men in the country," the population mean (μ) is the **true average height of every single man in the country**.

    *   If your population is "all widgets produced by a factory," the population mean (μ) is the **true average weight of every widget ever produced**.

---

### 2. What is the Sample Mean?


*   **Definition:** The sample mean (denoted by **x̄**, "x-bar") is the average of a specific characteristic calculated from a **subset** (a sample) taken from the population.

*   **The Tool:** Since we can't measure the entire population, we use the sample mean as an **estimate** for the population mean.


    **Examples (following the ones above):**

    *   You measure the height of 100 randomly selected men. Their average height is 180 cm. This 180 cm is your sample mean (x̄). It's your **best guess** for the true population mean (μ).

    *   You weigh 50 randomly selected widgets. Their average weight is 102 grams. This 102 grams is your sample mean (x̄), used to estimate the true average weight of all widgets (μ).


---


### 3. The Relationship: Population Mean (μ), Sample Mean (x̄), and Sample Size (n)


The relationship is governed by one of the most important concepts in statistics: **sampling distribution**.


#### a) The Sample Mean is an Estimate of the Population Mean


*   The fundamental idea is: **x̄ is an unbiased estimator of μ**.

*   This means that if you were to take every possible sample of size `n` from the population and calculate the mean for each one, the average of all those sample means would be exactly equal to the population mean (μ).


#### b) How Sample Size (`n`) Affects the Accuracy of the Estimate


This is where sample size becomes critical. The connection is explained by the **Standard Error (SE)**.


*   **Standard Error Formula:** \( SE = \frac{\sigma}{\sqrt{n}} \)

    *   `σ` (sigma) is the population standard deviation (how spread out the population data is).

    *   `n` is the sample size.


*   **The Key Insight:** The Standard Error measures the **typical distance** you can expect between a sample mean (x̄) and the true population mean (μ). It's the "margin of error" you'd naturally expect from sampling.


Let's see what happens when we change the sample size (`n`):


*   **Small Sample Size (e.g., n=10):**

    *   \( SE = \frac{\sigma}{\sqrt{10}} \) is a relatively large number.

    *   This means sample means from small samples can be **quite far** from the true population mean. Your estimate is **less precise and more volatile**.


*   **Large Sample Size (e.g., n=1000):**

    *   \( SE = \frac{\sigma}{\sqrt{1000}} \) is a much smaller number.

    *   This means sample means from large samples will **cluster much more tightly** around the true population mean. Your estimate is **more precise and reliable**.


---


### Summary with an Analogy: The Soup Pot


Imagine a giant pot of soup (the **population**).


*   The **population mean (μ)** is the *true average saltiness of the entire pot*.

*   You can't drink the whole pot to find out, so you use a spoon to take a taste (this is taking a **sample**).

*   The saltiness of the spoonful you taste is the **sample mean (x̄)**.


**How does spoon size (sample size `n`) matter?**


*   **Small Spoon (n is small):** A single tiny taste might be too salty or too bland compared to the whole pot. Your estimate is unreliable.

*   **Large Ladle (n is large):** A big taste is much more likely to represent the overall saltiness of the entire pot. Your estimate is reliable.


**The Central Limit Theorem** makes this even more powerful, stating that as your sample size gets larger, the distribution of all possible sample means (x̄'s) will form a normal distribution centered around the true population mean (μ), with a spread defined by the Standard Error. This is why we can create confidence intervals and make robust inferences about the population.



Saturday, October 4, 2025

Statistics: Standard Error and Central Limit Theorem

What is standard error of a population? 


Step 1: Definition of standard error

The standard error of the sample mean is:


Standard Error = σ / root(n) 

where  σ  is the population standard deviation and n n is the sample size.


Step 2: Can it be negative? No because standard deviation is always positive and n also be, so, standard error cannot be negative 


A survey about mental health has been conducted on the freshmen class at ABC High School. A sample of  200 students was randomly selected from the freshmen class at ABC High School for the survey. Identify the population in this study



The 200 selected students

All freshmen at ABC High School

All students at ABC High School


Step 1: Understand the terms

Population: The entire group of individuals the study is interested in learning about.

Sample: A subset of the population that is actually surveyed or studied.


Step 2: Identify the population in the question

The survey is about mental health of the freshmen class at ABC High School.

They took a sample of 200 students from the freshmen class.


So:


Population = All freshmen at ABC High School

Sample = The 200 selected students


Central Limit Theorem 


Let's break this down carefully.


---


### **1. What the Central Limit Theorem (CLT) says**

The CLT states that if you take random samples of size \( n \) from **any population** with mean \( \mu \) and finite variance \( \sigma^2 \), then as \( n \) becomes large, the sampling distribution of the sample mean \( \bar{X} \) approaches a **normal distribution** \( N(\mu, \sigma^2/n) \), regardless of the population's original distribution.


---


### **2. Does it matter if the population distribution is continuous or discrete?**

- **No** — the CLT applies to **any population distribution** with finite variance, whether it is **continuous** (e.g., height, weight) or **discrete** (e.g., number of children, test scores, dice rolls).

- The only requirement is:  

  1. Independent and identically distributed (i.i.d.) samples.  

  2. Finite variance \( \sigma^2 \).  

  3. Sample size \( n \) sufficiently large (rule of thumb: \( n \geq 30 \) for strong non-normality, but smaller \( n \) may suffice if population is not too far from normal).


---


### **3. Examples of CLT with discrete distributions**

- Rolling a fair die: population distribution is discrete uniform. The sample mean of many rolls will be approximately normal for large \( n \).

- Bernoulli trials: proportion of successes → approximately normal for large \( n \) (this is actually the De Moivre–Laplace theorem, a special case of CLT for binary data).


---


### **4. Conclusion**

The CLT holds for **both continuous and discrete distributions**.


---


\[

\boxed{\text{Continuous and Discrete distributions both}}

\]



Thursday, October 2, 2025

What is Google AgentSpace?

 AgentSpace is a dedicated, enterprise-grade platform designed by Google (often integrated within Vertex AI) for the complete lifecycle management of complex, autonomous AI Agents.


It moves AI Agents—which are programs built on Large Language Models (LLMs) like Gemini that can reason, plan, and use external tools/APIs—from research prototypes into reliable, scalable, and governed business solutions.


Think of AgentSpace as the operating system or orchestration layer for your organization's fleet of AI assistants. It provides the tooling necessary to manage the complexity that comes from agents making decisions and taking actions autonomously.


What is AgentSpace?

AgentSpace provides a centralized environment for four core functions related to AI Agents:


Building and Iteration: It offers frameworks and templates to define an agent's reasoning capabilities, its permitted external tools (APIs, databases), and its core mission (e.g., "The Customer Service Agent").


Deployment: It handles the transition from a development environment to a production environment, ensuring the agent is containerized, secure, and ready to handle high traffic.


Governance and Safety: It allows developers to define guardrails and constraints to ensure the agent's actions are safe, ethical, and comply with corporate policy.


Monitoring and Evaluation: It continuously tracks the agent's performance, latency, failure rates, and reasoning paths, allowing for rapid debugging and improvement.


How AgentSpace Benefits Enterprises

The value of AgentSpace lies in solving the specific challenges that arise when autonomous AI agents are integrated into critical business operations:


1. Robust Governance and Auditability

In an enterprise, every system action must be traceable. Since an AI agent makes its own decisions (e.g., calling an internal API or creating a ticket), strict control is necessary.


Benefit: AgentSpace provides detailed logging and audit trails for every action an agent takes, every tool it calls, and every internal reasoning step. This ensures regulatory compliance and provides a clear chain of accountability.


Safety Guards: It allows the enterprise to define security parameters—what APIs the agent is allowed to call, what data tables it is prohibited from accessing—thereby mitigating security and compliance risks.


2. Scalability and Reliability (Observability)

An agent that works well in testing must scale to handle thousands or millions of user interactions.


Benefit: AgentSpace is built on cloud infrastructure designed for massive scale. It handles load balancing and resource allocation automatically. More importantly, it provides deep observability tools (dashboards, metrics) that track agent performance in real-time. This helps enterprises quickly identify and fix issues like agents getting stuck in loops, using outdated information, or generating high-latency responses.


3. Accelerated Time-to-Value

Building a complex, custom agent often involves stitching together multiple tools, models, and data sources.


Benefit: The platform provides pre-integrated tools and frameworks that simplify the creation of complex agents. By managing the underlying infrastructure, versioning, and deployment logic, AgentSpace dramatically reduces the time required for developers to move an agent from a concept to a reliable production service. This means faster delivery of capabilities like automated triage, complex data analysis assistants, and autonomous execution of workflows.

What is Gemini Gems ?

A "Gem" is essentially a dedicated, personalized workspace powered by the Gemini model. You can think of it as your own private, tailored AI assistant created for a specific purpose or project.


The core idea behind Gems is to give users control over the scope and focus of their conversations, offering a middle ground between a general public chat and a highly customized application.


Key Characteristics of Gems:

Specialization: You can create a Gem with a specific persona and instructions. For example:


A "Coding Coach" Gem focused only on Python and Docker.


A "Travel Planner" Gem focused only on itinerary creation and logistics.


A "Creative Writer" Gem focused on fiction and storytelling.


Isolated Context: A Gem maintains its own history and context, separate from your main Gemini chat history. This isolation helps keep conversations focused and prevents context from bleeding across unrelated topics.


Efficiency: Because the Gem has a defined role, it is often more efficient and accurate in responding to specialized prompts within that domain.


What is "Saved Info in Gems"?

"Saved Info" is the feature that allows you to provide a Gem with long-term, persistent context and preference data that it uses across all your future interactions with that specific Gem.


This is fundamentally different from standard chat history, where the model only remembers what was discussed in the current thread.


The Purpose of Saved Info:

Personalized Grounding: You can input explicit, private data that the Gem should always reference.


Consistent Persona: The Gem can use this information to maintain consistency and relevance over time.



In short, Gems are the personalized chat environments, and Saved Info is the specific, long-term memory that makes each Gem uniquely useful to you by eliminating the need to repeat your preferences in every new conversation.



Wednesday, October 1, 2025

Google Cloud Learning - GenMedia MCP server

You can use the Firebase MCP server to give AI-powered development tools the ability to work with your Firebase projects. The Firebase MCP server works with any tool that can act as an MCP client, including Claude Desktop, Cline, Cursor, Visual Studio Code Copilot, Windsurf Editor, and more.

An editor configured to use the Firebase MCP server can use its AI capabilities to help you:


Create and manage Firebase projects

Manage your Firebase Authentication users

Work with data in Cloud Firestore and Firebase Data Connect

Retrieve Firebase Data Connect schemas

Understand your security rules for Firestore and Cloud Storage for Firebase

Send messages with Firebase Cloud Messaging



MCP Servers for Genmedia x Gemini CLI


What is the "Genmedia x Gemini CLI" Context?

Before defining MCP, let's look at the components:


Gemini CLI: The command-line interface used to interact with the Gemini model family, allowing developers and users to trigger GenAI tasks, deploy models, and manage input/output data.


Genmedia: This is a term likely referring to a suite of Google Cloud Media Services or applications focused on Generative Media (handling, processing, and generating video, audio, and high-resolution images). These workloads are extremely resource-intensive.


The MCP Servers are the dedicated backbone for the "Genmedia" part of the equation.


The Role of MCP Servers (Media-Optimized Compute)

While "MCP" can have various meanings, in this high-performance context, it is inferred to stand for a specialized compute platform, potentially Media Compute Platform or similar proprietary internal terminology.


These servers are designed to address the unique challenges of generative media:


1. High-Performance Hardware

These are not general-purpose virtual machines. MCP Servers would be provisioned with specialized hardware necessary to run state-of-the-art media and AI models efficiently:


GPUs/TPUs: They are powered by massive arrays of Graphics Processing Units (GPUs) or Tensor Processing Units (TPUs), which are essential for the parallel computations required by large transformer models like Gemini.


Large Memory and VRAM: Generative media tasks (especially video) require large amounts of Video RAM (VRAM) and system memory to hold both the large models and the massive input/output files.


2. High Throughput & Low Latency

Processing a 4K video or generating several minutes of complex animation requires moving terabytes of data quickly.


High-Speed Networking: MCP Servers are equipped with extremely high-bandwidth networking (often 100Gbps or higher) to minimize the latency involved in reading media from storage, running it through the model, and writing the result back.


Optimized Storage: They often interface directly with low-latency, high-throughput storage systems tailored for media workloads.


3. Dedicated Workloads for Genmedia

When you use the Gemini CLI to initiate a video generation task (a Genmedia workload), the system transparently routes that request to these specialized MCP Servers because they are the only infrastructure capable of completing the task economically and quickly