# How to find distribution of some statistics for i.i.d. normal random variables?

Let $Y=(Y_1,Y_2,\ldots,Y_n)^{T}$ and $Y_1,\ldots,Y_n$ are independent normal random variables with mean $0$ and variance $\sigma^2$. Find the distribution of the following statistics and give your reasons

a) $T=\displaystyle \sum_{i=1}^{6}(Y_i-\overline{Y})^2$

b) $U =\displaystyle\frac{\sqrt{5}\times Y_6}{\sqrt{Y_{1}^2+Y_{2}^2+Y_{3}^2+Y_{4}^2+Y_{5}^2}}$