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Contents Uniform Distribution Mean and Variance Normal (Gaussian) Distribution Possibility Desnity Function(PDF) Cumulative Distribution Function(CDF) Uniform Distribution If the probability density function of a random variable X is constant over the range [a, b] as in Equation 1, then the variable is said to be uniformly distributed. $$\begin{align}\tag{1}f(x)=\begin{cases}\frac{1}{b-a}& \quad a \lt x \lt b\\ 0&\quad \text{otherwise} \end{cases}\end{align}$$ A uniform distribution is expressed as $$X \sim \text{Uniform(a, b)}$$ Example 1)   If the variable X is uniformly distributed in the range [0,10], try calculating the following probabilities: $$\begin{align}&f(x)=\frac{1}{10-0}\\&F(x)=\int^b_a \frac{1}{10-0} \, dx \quad 0 \le a \lt b \le 10 \end{align}$$ import numpy as np import pandas as pd from sympy import * import matplotlib.pyplot as plt from scipy import stats a, b, x=symbols("a b x") f=Rational(1, 10) f $\quad \colo...