Let Y, Y2..... Y5 be a random sample of size 5 from a normal population with mean 0 and variance 1 and let = Let Yo be another independent observation from the same population. Additionally let W X and UX be two more random variables independent from all other random variables. Find the distributions of the following random variables and explain your reasoning N (a) Y2 (b) U=(Y-Y) (c) 5Y (d) 5Y6/W (e) 2Y6/U (f) V=Y-2Y +3 (g) 2(5 + Y)/U