<b> INFERENTIAL STATISTICS </b>
    
It help us to get the inferences about the population from picking out the samples from the population.
    
It's helps to estimate thr natural parameters of a probability distribution followed by the population. Estimate can be good or bad both types. 
    
The propoerties of the good estimator is:
<ol>
<li> It should be unbiased. </li>
<li> It should have minimum variance </li>
</ol>

<b> Frequency Distribution </b> of any sample statistics plotted by doing repeated sampling is called sampling distribution of that sample statistics.

<b> Central Limit Theorem </b>

Central Limit Theorem states that the frequency distribution of a sample statistics approaches pure normal distribution as the N (sample size) approaches to the infinity as well as the variance of the sampling distribution  of a sample statistics is inversely proportional to the N (sample size).

Variance of a sampling distibution of sample statistics is inversely proportional to sample size (N).

\begin{equation}
Variance\ of\ a\ sampling\ distribution\\ of sample\ statistics\ (\sigma^2) = \frac{\sigma^2}{N} 
\end{equation}
<br>

\begin{equation}
Standard\ deviation\ of\ a\ sampling\ distribution\\ of sample\ statistics\ (\sigma) = \frac{\sigma}{\sqrt(N)} 
\end{equation}

<b> Why we make sampling distibution? </b><br>
To get the:

Best Estimator = Minimum Variance Unbiased (MVU) Estimator

<b> Python code to prove the central limit theorem::: </b>

Let's check it using by taking an example of the coin tossing. 


```python
import numpy as np
import pandas as pd
```


```python
N = 10
psuccess = 0.5
qfailure = 1-psuccess
ExperimentOutcomes = np.random.binomial(N,psuccess)
```


```python
ExperimentOutcomes
```




    6




```python
N = 100
ExperimentOutcomes = np.random.binomial(N,psuccess)
```


```python
ExperimentOutcomes
```




    49



It will stablize the value of the sample size will increase. As we know that the probability of the getting the head/tail in coin tossing is 50 % i.e., 0.5. 


```python
N = 10000000
ExperimentOutcomes = np.random.binomial(N,psuccess)
```


```python
ExperimentOutcomes
```




    4999066




```python

```

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ipynb
Jupyter Notebook
5. Inferential Statistics.ipynb
rarpit1994/Probability-and-Statistics
1ae8b7428ec9a3072fce3089d7951b9f7bd06c26
Apache-2.0
2019-03-24T10:29:56.000Z
2019-03-24T10:29:56.000Z
5. Inferential Statistics.ipynb
rarpit1994/Probability-and-Statistics
1ae8b7428ec9a3072fce3089d7951b9f7bd06c26
Apache-2.0
5. Inferential Statistics.ipynb
rarpit1994/Probability-and-Statistics
1ae8b7428ec9a3072fce3089d7951b9f7bd06c26
Apache-2.0
Qwen/Qwen-72B
1. YES
2. YES