Suppose that the joint density function for two continuous random

variables X and Y is defined by

f_X;Y (x; y) = cx²y⁵, if 0 < x; y < 1

f_X;Y (x; y) = 0, otherwise

(a) Determine the value of c.

(b) Determine the joint (cumulative) distribution function

F_X;Y (x; y) = P(X <= x; Y <= y) of X and Y .

(c) Determine the (marginal) density functions f_X(x) and f_Y (y).

(d) Are X and Y independent random variables? Justify your answer.

(e) Calculate P(X <= 0.25, Y <= 0.75) .