Suppose that five balls are sampled with replacement from an urn that contains 10 red balls, 10 blue balls, 5 green balls and 5 yellow balls and let R, B, G and Y, respectively, denote the numbers of red, blue, green or yellow balls in the sample.
 

(a) Find the joint probability mass function of (R, B,G,Y). (b) Find the probability mass functions of B and of R+ G. (c) Calculate E[G+Y 2 * R]. (d) Calculate Cov(R+G, B +Y).