1. A certain market has both an express checkout line and a super express 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 super express checkout at the same time. Suppose the joint pmf of Xı and X2 is as given in the accompanying table. X2 1 2 3 0.08 0.07 0.04 0.03 1 0.07 0.10 0.08 0.04 X, 2 0.05 0.04 0.06 0.05 3 0.01 0.04 0.04 0.07 4 0.02 0.01 0.05 0.05 (a) What is P(X, < X,)?

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1. A certain market has both an express checkout line and a super express 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 super
express checkout at the same time. Suppose the joint pmf of X1 and X2 is as given in
the accompanying table.
X,
1
2
0.08
0.07
0.04
0.03
1
0.07
0.10
0.08
0.04
X, 2
0.05
0.04
0.06
0.05
3
0.01
0.04
0.04
0.07
0.02
0.01
0.05
0.05
(a) What is P(X, < X2)?
(b) What is the marginal distribution of X1 ?
Transcribed Image Text:1. A certain market has both an express checkout line and a super express 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 super express checkout at the same time. Suppose the joint pmf of X1 and X2 is as given in the accompanying table. X, 1 2 0.08 0.07 0.04 0.03 1 0.07 0.10 0.08 0.04 X, 2 0.05 0.04 0.06 0.05 3 0.01 0.04 0.04 0.07 0.02 0.01 0.05 0.05 (a) What is P(X, < X2)? (b) What is the marginal distribution of X1 ?
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