Moment-generating function of a chi-squared distribution
= Moment-generating function of a chi-squared distribution
{title2=$M_{\chi_n^2}(t)=(1-2t)^{-n/2}$}
A sum of the squares of $n$ <independent random variables> with the <standard normal distribution> has the <chi-squared distribution> with $n$ degrees of freedom. A scaled <Gaussian integral> and factorization by independence give its <moment-generating function> $(1-2t)^{-n/2}$ for $t<1/2$. For positive $n$, this <expectation> diverges when $t\geq1/2$.