There is a 76 % chance that when a shopper sees product X in the store, the shop

Question

There is a 76 % chance that when a shopper sees product X in the store, the shopper will like it. If a shopper likes it he or she will buy one. If the shopper does not like it, he or she will buy zero. Mrs. Smith has just seen product X. Express your answers to four decimal points. Express your answers as decimals- not as percentages. a. What is the expected value of the number of units of product X that Mrs. Smith will buy? b. What is the variance of the number of units of product X that Mrs. Smith will buy? Enter your answer in each of the answer boxes. 26

Explanation / Answer

let Y is number of units that mrs smitth will buy

as she will buy one if she likes the product

so

P(Y=1) =0.76

P(Y=0) =0.24

a)

We have to find E(Y)=?

now

E(Y) =1*P(Y=1) +0*P(Y=0) =1*0.76+0*0.24 =0.76

b)

E(Y2) =12P(Y=1) +02P(Y=0) =0.76

so

Var(Y) =E(Y2)-(E(Y))2= 0.76 -(0.76)2=0.76 -0.5776=0.1824

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