a. What is P(Xi= 1, X2= 1), that is, the probability that there is exactly one customer in each line? b. What is P(Xı=X2), that is, the probability that the numbers of customers in the two lines are %3D 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 Xı and X2, and calculate the probability of this event.

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Chapter1: Combinatorial Analysis
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A certain market has both an express checkout line and a superexpress checkout line. Let Xı
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 Xi and X2 is as given in the accompanying table.
X2
1
3.
08
.07
.04
00
X1
06
15
05
04
2
05
.04
.01
06
00
03
.04
07
4
.00
101
05
06
a. What is P(X1= 1, Xz= 1), that is, the probability that there is exactly one customer in each
line?
b. What is P((Xı=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 Xı and X2, and calculate the probability of this event.
d. What is the probability that the total number of customers in the two lines is exactly four? At
least four?
Transcribed Image Text:A certain market has both an express checkout line and a superexpress checkout line. Let Xı 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 Xi and X2 is as given in the accompanying table. X2 1 3. 08 .07 .04 00 X1 06 15 05 04 2 05 .04 .01 06 00 03 .04 07 4 .00 101 05 06 a. What is P(X1= 1, Xz= 1), that is, the probability that there is exactly one customer in each line? b. What is P((Xı=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 Xı and X2, and calculate the probability of this event. d. What is the probability that the total number of customers in the two lines is exactly four? At least four?
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