A local Safeway supermarket has both an express checkout line and a super-expres

Question

A local Safeway supermarket has both an express checkout line and a super-express checkout line. Let X_1 denote the number of customers in the express checkout line at a particular time of day. Let X_2 denote the number of customers in the super-express checkout line at a particular time of day. The joint pmf for the random variables is: a. What is the probability that there is exactly one customer in each line? b. What is the probability that there is exactly one customer in line? c. What is the probability that the number of customers in the express line is the same as the number of customers in the super-express line? d. Find the expected number of customers in line.

Explanation / Answer

a

P(Exactly one customer in each line) = P(X1= 1, X2=1) = 0.15

b)

P(Exactly one customer in line) = P(X1= 1, X2=0) + P(X1= 0, X2=1) + = 0.07+0.06 = 0.13

c)

P(number of customers in the express line is same as number of customers in super-express line)

= P(X1=0, X2=0) + P(X1=1, X2=1) + P(X1=2, X2=2) +P(X1=3, X2=3)

= 0.08+0.15+0.10+0.07 = 0.40

d)

Number of Customers Probability x*P(x) 0 0.08 0 1 0.13 0.13 2 0.24 0.48 3 0.09 0.27 4 0.17 0.68 5 0.11 0.55 6 0.12 0.72 7 0.06 0.42 Expected number of customers = 3.25

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