Normal, Chi-Squared and Gamma Distributions
Here we show the classical example on how the normal, chi-squared, and gamma distributions are related. If Z_1, \ldots, Z_n are i.i.d. variables with the standard normal distribution, then \sum_{i=1}^n Z_i \sim \chi^2_n. Let X_1, \ldots, X_n \sim \text{Normal}(\mu, \sigma^2) …