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Moment generating function on normal distribution

Use the method of moment generating function to prove that if $X$ follows a standard normal function then $X^2$ follows a chi-square distribution. My question is how is this possible? I thought the method of MGF only applies to sums of independent variables?

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Ask Mathematics

Moment generating function on normal distribution

Use the method of moment generating function to prove that if $X$ follows a standard normal function then $X^2$ follows a chi-square distribution. My question is how is this possible? I thought the method of MGF only applies to sums of independent variables?