a. Recalling the definition of σ2 for a single rv X, write a formula that would be appro...

a. Recalling the definition of σ² for a single rv X, write a formula that would be appropriate for computing the variance of a function h(X, Y) of two random variables. [Hint: Remember that variance is just a special expected value.]

b. Use this formula to compute the variance of the recorded score h(X, Y) [ = max(X, Y)] in part (b) of Exercise 22.

Reference exercise 22

An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y =the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table.

a. If the score recorded in the grade book is the total number of points earned on the two parts, what is the expected recorded score E(X + Y)?

b. If the maximum of the two scores is recorded, what is the expected recorded score?