Let Z be a standard normal random variable: i.e., Z ~ N(0,1). (1) Find the pdf of U = Z2 from its distribution. (2) Given that f(1/2) = VT Show that U follows a gamma distribution with parameter a = 1 = 1/2. (3) Show that I (1/2) = V1. Note that I (1) = Soe ex-1/2dx. Hint: Make the change of variables y = V2x and then relate the resulting expression to the normal distribution.
