Solution

Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 32 / 1 / a / ii / Solution

{title2=$\chi^2_\nu(\lambda)$}

If $Z_1,\ldots,Z_\nu$ are independent <standard normal random variables> and $\lambda=\sum_j\mu_j^2$, then $\sum_j(Z_j+\mu_j)^2$ has a noncentral chi-squared distribution with $\nu$ degrees of freedom and noncentrality $\lambda$. For $\lambda=0$ it reduces to the <chi-squared distribution>. Squaring a shifted <signed normal Wald statistic> gives the case $\nu=1$.

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 Incoming links: Noncentral chi-squared distribution