Let X u...,Xn be independently, identically distributed N(|x,a2). Show that U = 2, 2y {Xj - Xj)2 and W = 2f=1 X t are independent. Find the distribution of U.  Show that if X , Y are independent...

Let X u...,Xn be independently, identically distributed N(|x,a2). Show

that U = 2, 2y {Xj - Xj)2 and W = 2f=1 X t are independent. Find the

distribution of U.

 Show that if X , Y are independent random variables (univariate) such

that X + Y is independent of X - Y, then both X and Y are normal

random variables.