Assume that you have random variable X with the following probability density function with a > 0, b > 0: r(a+b) fx (x) = Majora-1(1 -x)6-1 ifce (0, 1) 0 otherwise. (a) Suppose that a = 2 and b = 2. In this case, derive E X] and var[X"]. (b) Continuing with the X from part (a) with a = 2 and b = 2, let Z X = x ~ Binomial(n, x). Find E[ Z) and var [Z]. (c) Find the probability density function of Y defined by the following transfor- mation: X Y = 1 - X