# $Y \sim N_n (0,\sigma^2 I_n)$, find conditional distn of $Y'Y|a'Y=0$

Given that $Y$ follows multivariate normal distribution ,i.e, $N_n (0, \sigma^2 I_n)$, we want to find the distribution of $Y'Y$ given that $a'Y=0$ where $a$ is a non zero constant vector.

I know that the distribution of $Y'Y$ would be $\sigma^2 \chi_n^2$if the condition is not given. How to approach for the given condition.

Thanks.

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@anonymous user: If you are the OP, please log in and edit your question. If you are not, post your suggested edit as a comment. –  Julian Kuelshammer Dec 2 '12 at 20:14