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}}

\]