xercis Suppose X, Y have joint density function
.11:7(xy ± y2), .f (x, = o,
0 < x < 1 and 0 < y < 1 otherwise.
(a) Check that f is a genuine joint density function. (b) Find the marginal density functions of X and Y. (c) Calculate the probability P(X < Y). (d) Calculate the expectation E[X2 238 Joint distribution of random variables Exercise 6.6. Suppose that X, Y are jointly continuous with joint probability density function xe-41+54 , if x > 0 and y > 0 f(x,y) = 0, otherwise. (a) Find the marginal density functions of X and Y. (b) Calculate the expectation MY]. (c) Calculate the Pv Potntinn Fr x 1