probability theory

2. Two discrete random variables X and Y have the joint cumulative distribution function (cdf) defined as 1/12 x = 0,y =0 1/3 x =0,y =1 2/3 x=0,y = 2 Fxy (x, y) = 1/6 x =1,y=0 7/12 x = 1,y =1 = 1,y = 2 (a) Obtain i. the marginal cdfs of X and Y, ii. the joint probability mass function (pmf) of X and Y, iii. the conditional pmf of Y given X = 0 and X = 1. (b) Define the random variable Z = E[X|Y], provide the pmf of Z