Chi-Squared \((\chi^2)\) Distribution

The chi-squared distribution describes the probability distribution of the sum of squared independent and identically distributed standard normal random variables, commonly used in statistical hypothesis testing and confidence interval calculations.

An \(\chi^2\) random variable is denoted as followed:

\[ X \sim \chi^2(p) \]

Note that the exponential distribution is a gamma distribution that can be modeled as such:

\[ X \sim \text{Gamma}(\frac{p}{2}, 2) \]