1/ Let X1 and X2 be two independent random variables each with probability density function

1/ Let X1 and X2 be two independent random variables each with probability density function fXi(xi) = e-xi, for xi> 0 for i = 1,2. (a) Find the joint probability density function of X1 and X2. (b) Find P(X1 > 1, X2 < 1). (c) Find P(X1 + X2 < 2). 2/ Let X be a continuous variable with probability density functionf(x) = kx(1 - x)2with 0 < x < 1, 0 otherwise. (a) Find a value of k so that f(x) is a proper density. (b) Find the cumulative distribution function of X. (c) Find P(0. 25 < X < 0. 75 | X > 0. 5).