Let X be a random variable with density fX(t) = t(t 2 3 )1[+1,+1] with , R, > 0. (a) Find in terms of . (b) Find the cumulative distribution function of X. (c) Calculate P( < X 1). (d) Consider g : RRdefined as g : x 7x3, i.e. g(x) = x3. What is the probability density function of the random variable Y := g(X)