Let X denote a random variable supported on [0, 1] with pdf f (x) = c x2, where c is some constant. This question has to be answered analytically without using R. (a) Compute the value of c. (b) Write down the CDF of X . (c) Write down the quantile function of X , and compute its median. (d) Compute E[X ] and Var[X ]. (e) Let Y = pX . Compute E[Y ] and Var[Y ]