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** **)** *= *./**2**e-"-** **)**,** *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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