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. *2 1 2 3 0.09 0.07 0.04 0.00 1 0.05 0.15 0.05 0.04 0.05 0.04 0.10 0.06 0.01 0.02 0.04 0.07 4 0.00 0.02 0.05 0.05 (a) What is P(X, = 1, X2 = 1), that is, the probability that there is exactly one customer each line? P(X, = 1, X, = 1) = [ (b) what is P(X, - X), that is, the probability that the numbers customers in the two lines are identical? P(X, = x2) = [ (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 X, and X3. O A = (X, 2 2 + X, U X2 2 2 + X,> O A= (X, s2 + Xg u X2 2 2 + X,) O A = {X, s 2 + X, UXg $ 2 + X;> O A (X, 2 2 + X, U Xz s 2 + X,} Calculate the probability of this event. P(A) = [
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. *2 1 2 3 0.09 0.07 0.04 0.00 1 0.05 0.15 0.05 0.04 0.05 0.04 0.10 0.06 0.01 0.02 0.04 0.07 4 0.00 0.02 0.05 0.05 (a) What is P(X, = 1, X2 = 1), that is, the probability that there is exactly one customer each line? P(X, = 1, X, = 1) = [ (b) what is P(X, - X), that is, the probability that the numbers customers in the two lines are identical? P(X, = x2) = [ (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 X, and X3. O A = (X, 2 2 + X, U X2 2 2 + X,> O A= (X, s2 + Xg u X2 2 2 + X,) O A = {X, s 2 + X, UXg $ 2 + X;> O A (X, 2 2 + X, U Xz s 2 + X,} Calculate the probability of this event. P(A) = [
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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Transcribed Image Text: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
0.09
0.07
0.04
0.00
1
0.05
0.15
0.05
0.04
X1
0.05
0.04
0.10
0.06
0.01
0.02
0.04
0.07
4
0.00
0.02
0.05
0.05
(a) What is P(X, = 1, X, = 1), that is, the probability that there is exactly one customer in each line?
P(X, = 1, X, = 1) = |
(b) What is P(X, = x,), that is, the probability that the numbers of customers in the two lines are identical?
P(X, = X,) =
(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 X, and X,.
O A = {X, 2 2 + X2U X, 2 2 + Xq}
O A = {X, s 2 + X2 U Xq 2 2 + Xq}
O A = {X, s 2 + X2 U Xq S2+ Xq}
O A = {X, 2 2 + X2 U Xq S2+ Xq}
Calculate the probability of this event.
P(A) =
(d) What is the probability that the total number of customers in the two lines is exactly four? At least four?
P(exactly four) =
P(at least four) = |
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