Suppose Y1, Y2, ... Y10 are iid normal with mean = 0 and variance > 0.

Suppose Y1, Y2, . . .Ylo are iid normal with mean a = 0 and variance 02 > U. (a) Let Z : Yl + Y2 + Y}; + H. Then derive the distribution of 2'. Be sure to not just state the distribution of Z but also its derivation. (b) Let V 2 Y5\") + Y? + YE? + YE? + 1'? + 371%. Then derive the distribution of %. 252 13/6- (c) Describe the distribution of the random variable (d) Find the value for c for which 131% g c) = 0.95