November 8, 2017 Math 311 Exam 2 Please whateve as much work as you can, unless

Question

November 8, 2017 Math 311 Exam 2 Please whateve as much work as you can, unless a one-sided sheet of notes on standard letter-sized paper. write your solutions in the blue books distributed to you. You can put your solutions in r order you like, but make sure you number your solutions so I know which is which. Show otherwise specified. Calculators are not permitted. You may use nts I. Each customer who enters a store has an independent l0% chance of making a purchase. (a) Let X be the number of customers out of the first 10 who make a purchase. Find P(2 SX in that form. Do not try to evaluate your answer. You may leave an expression like ( 4 (b) Find E(x). (c) Let Y be the number of customers who fail to make a purchase before the first purchase occurs. Find P(Y 2 4). Do not try to evaluate your answer. (d) Find E(Y) (e) Let Z be the number of the customer who makes the first purchase (e.g.. 1 if customer makes a purchase). Find E(Z)

Explanation / Answer

a) Given n = 10, p = 0.10

P(2<= X<= 4) = 0.262266134

b) E(X) = np = 10*0.10= 1

c) P(Y>=4) = 0.012795198

d) E(Z) = 1/p = 1/0.1 = 10

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