3. A certain market has both an express checkout line and a superexpress checkout line. Let X, denote the number of customers in line at the express checkout at a particular time of day, and let X, denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X, and X, is as given in the accompanying table. X2 1 2 3 .08 .07 .04 .00 .06 .15 .05 .04 .05 .04 .10 .06 .00 .03 .04 .05 07 4 .00 .01 .06 a. What is P(X, = 1. X, = 1), that is, the probability that there is exactly one customer in each line? b. What is P(X,= X), 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 cus- tomers in one line than in the other line. Express A in terms of X, and X, and calculate the probability of this event. 01130

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3. A certain market has both an express checkout line and a
superexpress checkout line. Let X, denote the number of
customers in line at the express checkout at a particular
time of day, and let X, denote the number of customers in
line at the superexpress checkout at the same time. Suppose
the joint pmf of X, and X, is as given in the accompanying
table.
X2
1
3
.08
.07
.04
„00
1
.06
.15
.05
.04
.05
.04
10
.06
3
.00
.03
04
07
4
.00
.01
.05
.06
a. What is P(X, = 1, X, = 1), that is, the probability that
there is exactly one customer in each line?
b. What is P(X, = X), 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 cus-
tomers in one line than in the other line. Express A in
terms of X, and X, and calculate the probability of this
event.
Transcribed Image Text:3. A certain market has both an express checkout line and a superexpress checkout line. Let X, denote the number of customers in line at the express checkout at a particular time of day, and let X, denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X, and X, is as given in the accompanying table. X2 1 3 .08 .07 .04 „00 1 .06 .15 .05 .04 .05 .04 10 .06 3 .00 .03 04 07 4 .00 .01 .05 .06 a. What is P(X, = 1, X, = 1), that is, the probability that there is exactly one customer in each line? b. What is P(X, = X), 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 cus- tomers in one line than in the other line. Express A in terms of X, and X, and calculate the probability of this event.
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