Question: 4.69 Consider Review Exercise 3.77 on page 128. The random variables X and Y represent the number of vehicles that arrive at two separate street

4.69 Consider Review Exercise 3.77 on page 128. The random variables X and Y represent the number of vehicles that arrive at two separate street corners during a certain 2-minute period in the day. The joint distribution is f(x, y) =

1 4(x+y )

9 16

, for x = 0, 1, 2, . . . and y = 0, 1, 2, . . . .

(a) Give E(X), E(Y ), Var(X), and Var(Y ).

(b) Consider Z = X + Y , the sum of the two. Find E(Z) and Var(Z).

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