2. Let X and Y be jointly continuous random variables with joint pdf f(x, y) = c(alty? ) -1

2. Let X and Y be jointly continuous random variables with joint pdf -1 otherwise For your convenience, you may use without proof that the marginal pdf of Y is given by otherwise and that the mean and variance of X are E(X) O and Var(X) = respectively. 21 (a) Find value of the c that makes f (x, y) is a valid pdf. Note: If you are unable to to do parts (b)-(e). solve this part of the question, you may use the value c (3 pts) (b) Find the marginal distribution of X. (3 pts) (c) Are X and Y independent? Justify your answer. (3 pts)