```python
import sympy as sy
import scipy as sp
import numpy as np
import random as rd
import plotly as py
from ipywidgets import interact
from matplotlib import pyplot
from stat_dist import *
```

##### Gaussian distribution is:


$$ f(x; \mu, \sigma) = \frac{1}{\sqrt{2 \pi \sigma^2}}  e^{-\frac{(x-\mu)^2}{2\sigma}}$$

where $\mu$ is mean value ($1^{st}$ moment) and $\sigma$ is standard deviation (square rot of $2^{nd}$ moment).


```python
N = int(input())
l, r = map(float, input().split())
```


```python
def g(mu, sigma):
    x = gauss(mu-3*sigma, mu+3*sigma, mu, sigma, N)
    stat(x, mu-3*sigma, mu+3*sigma, 0.001, N)
    
interact(g, mu = (-10, 10, 0.01), sigma = (0.01, 10, 0.01))
```

#### Uniform distribution on set $\Omega$ is:

$$p(x; \Omega) = \frac{1}{\mu(\Omega)}$$

where $\mu(\Omega) = \int_{\Omega} d\mu$ is Lebesgue measure of a set $\Omega$. 

For example:
1. $\Omega = [a,b]$: $$p(x) = \frac{1}{b-a}$$,
2. $\Omega = \{a_1,a_2,...,a_N\}$: $$p(a_i) = \frac{1}{N}$$

and so on...




```python
N = int(input())
l, r = map(float, input().split())
x = uniform(l, r, N)
stat(x, l, r, 0.001, N)
```

#### Gamma distribution is:

$$f(x; \alpha, \beta) = \frac{\beta^{\alpha} x^{\alpha-1}e^{-\beta x}}{\Gamma(\alpha)}$$


```python
N = int(input())
h = float(input())
```


```python
def gam(alfa, beta):
    x = gamma(h, alfa, beta, N)
    stat(x, 0, h, 0.001, N)
    
interact(gam, alfa = (0.01, 10, 0.01), beta = (0.01, 10, 0.01))
```

stat_dist.py contains some more probability distribution functions, whose graphs can be constructed in the same maneer.


```python

```

fccfa85b75a15344f1852eca594bc84e8622b274
ipynb
Jupyter Notebook
Statistical Distributions/dist.ipynb
PhyProg/Scientific-Computing
cdbbbe67b7621c4cf2a2995c576bcbebbc65d1a6
MIT
Statistical Distributions/dist.ipynb
PhyProg/Scientific-Computing
cdbbbe67b7621c4cf2a2995c576bcbebbc65d1a6
MIT
Statistical Distributions/dist.ipynb
PhyProg/Scientific-Computing
cdbbbe67b7621c4cf2a2995c576bcbebbc65d1a6
MIT
Qwen/Qwen-72B
1. YES
2. YES