A certain market has both an express checkout line and a superexpress checkout line. Let Xıdenote the number of customers in line at the express checkout at a particular time of day, andlet X2 denote the number of customers in line at the superexpress checkout at the same time.Supposethe joint pmf of Xi and X2 is as given in the accompanying table.X213.08.07.0400X106150504205.04.01060003.04074.001010506a. What is P(X1= 1, Xz= 1), that is, the probability that there is exactly one customer in eachline?b. What is P((Xı=X2), that is, the probability that the numbers of customers in the two lines areidentical?c. Let A denote the event that there are at least two more customers in one line than in the otherline. 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? Atleast four?

As per our guidelines, we are allowed to answer first three sub-parts only. Thanks Given :

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.

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.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

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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