3.9.1. Suppose that r crups are drawn with replacement from an urn containing n chips, num bered 1 through n. Let V denote the sum of the numbers drawn. Find E(V ).
3.9.2. Suppose that fx.Y (X , y ) = ./2e-"- ), 0 .::: x , 0 :$ y . Find E( X + Y).
3.9.3. Suppose Lhat Jx.Y (X . y) = j' (X + 2y ), 0 ":: x :::. 1, 0 :$ y 5 1. (recall Question 3.7.19(c)).
Find E( X + Y).
3.9.4. Marksmanship competition at a certain level requires each contestant to take 10 shots with each of two different hand guns. Final scores are computed by taking a weighted average of four times the number of bull's-eyes made with the first gun plus six times the num ber gotten with the second. If Cathie has a 30% chance of hitting the bull's-eye with each shot from the first gun and a 40% chance with each shot from the second gun, what is her expected score?
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