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A market has both an express checkout line and a superexpress checkout line. Let X₁ denote the number of customers in line at the express checkout at a particular time of day, and let X₂ denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X₁ and X₂ is as given in the accompanying table. X1 b. 0 1 2 3 4 0 .08 .06 .05 .00 .00 1 .07 .15 .04 .03 .01 x2 2 .04 .05 .10 .04 .05 3 .00 .04 .06 .07 .06 a. What is P(X₁ = 2 and X₂ = 2), that is the probability that there is exactly one customer in each line? What is P(X₁ = X₂), that is, the probability that the numbers of customers in the two lines are identical? c. Let A denote the event that there are at least two more customers in one line than in the other line. Express A in terms of X₁ and X2, and calculate the probability of event A, that is P(A).

A market has both an express checkout line and a superexpress checkout line. Let X₁ denote the number of customers in line at the express checkout at a particular time of day, and let X₂ denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X₁ and X₂ is as given in the accompanying table. X1 b. 0 1 2 3 4 0 .08 .06 .05 .00 .00 1 .07 .15 .04 .03 .01 x2 2 .04 .05 .10 .04 .05 3 .00 .04 .06 .07 .06 a. What is P(X₁ = 2 and X₂ = 2), that is the probability that there is exactly one customer in each line? What is P(X₁ = X₂), that is, the probability that the numbers of customers in the two lines are identical? c. Let A denote the event that there are at least two more customers in one line than in the other line. Express A in terms of X₁ and X2, and calculate the probability of event A, that is P(A).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A market has both an express checkout line and a superexpress checkout line. Let X₁ denote the number of customers in line at the express checkout at a particular time of day, and let X₂ denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X₁ and X₂ is as given in the accompanying table. X1 0 1 2 3 4 b. 0 .08 .06 .05 .00 .00 1 .07 .15 .04 .03 .01 X2 2 .04 .05 .10 .04 .05 3 .00 .04 .06 .07 .06 a. What is P(X₁ = 2 and X₂ = 2), that is the probability that there is exactly one customer in each line? What is P(X₁ = X₂), that is, the probability that the numbers of customers in the two lines are identical? c. Let A denote the event that there are at least two more customers in one line than in the other line. Express A in terms of X₁ and X2, and calculate the probability of event A, that is P(A). d. Determine the marginal pmf of X₁, and then calculate the expected number of customers in line at the express checkout. e. Determine the marginal pmd of X2. f. Are X₁ and X₂ independent random variables? Explain.
Transcribed Image Text:A market has both an express checkout line and a superexpress checkout line. Let X₁ denote the number of customers in line at the express checkout at a particular time of day, and let X₂ denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X₁ and X₂ is as given in the accompanying table. X1 0 1 2 3 4 b. 0 .08 .06 .05 .00 .00 1 .07 .15 .04 .03 .01 X2 2 .04 .05 .10 .04 .05 3 .00 .04 .06 .07 .06 a. What is P(X₁ = 2 and X₂ = 2), that is the probability that there is exactly one customer in each line? What is P(X₁ = X₂), that is, the probability that the numbers of customers in the two lines are identical? c. Let A denote the event that there are at least two more customers in one line than in the other line. Express A in terms of X₁ and X2, and calculate the probability of event A, that is P(A). d. Determine the marginal pmf of X₁, and then calculate the expected number of customers in line at the express checkout. e. Determine the marginal pmd of X2. f. Are X₁ and X₂ independent random variables? Explain.
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