## 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 $$X_1, \ldots, X_n \sim \text{Normal}(\mu, \sigma^2)$$

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