Tutorials for Chi-square Distribution 2

Theorem 1: Let . Then, if , we say that X follows the chi-square distribution with 1-degree of freedom. We then write .

Proof.

or,

This is the PDF of , it is called the chi-square distribution with 1-degree of freedom, denoted by .

Note that the moment generating function of  is .

Theorem 2: Let  be independent random variables with . follows the chi-square distribution with n-degrees of freedom, denoted by .

Proof.

This is the moment generating function of , and it is called the chi-square distribution with n-degrees of freedom.

Note: