Question 2 [14 marks] A random variable X has probability density function f(x) = iz 0 x(2 -I) for 0 Do. 1= 1 (e) Assume that for any random variables U and V. 1) if U - u, then (2 P u2; 2) if U u, V Pv, then V - U v -u. Show that _ _ (x: - X)? _ Var(X) asn - Do. (f) Use the central limit theorem to find an approximate value to the probability /175x37 Pr() X? 2 212 x 37) Keep your answer in terms of cumulative distribution function (x) of N(0, 1)