Continuous random variable

Chi-squared distribution

A chi-squared distributed random variable is the sum of squares of independent and identically distributed with standard normal distributions. #m/def/prob

This turns out to be a special case of the Gamma distribution, namely .

Proof

Let for , i.e. . Then

thus

so . Thus by ^Q1, the claim is proven.

Properties

Additional properties

  1. Let be a random sample of variable independently distributed according to the normal distribution . Then the sample variance is distributed such that

#state/tidy | #lang/en | #SemBr