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customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X₁ and X₂ is as given in the accompanying table. x2 X1 0 1 2 3 4 0 1 2 3 0.07 0.04 0.00 0.09 0.05 0.15 0.05 0.04 0.05 0.04 0.10 0.06 0.00 0.03 0.04 0.07 0.00 0.02 0.05 0.05 (a) What is P(X₁ = 1, X₂= 1), that is, the probability that there is exactly one customer in each line? P(X₁ = 1, X₂= 1) = [ (b) What is P(X₁ = X₂), that is, the probability that the numbers of customers in the two lines are identical? P(X₁ = 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 X₁ and X₂- OA (X₁ 2 2 + X₂ U X₂ ≥ 2 + X₂} OA (X₁ ≤ 2 + X2₂ U X₂ ≤ 2 + X₂} OA (X₁ ≥ 2 + X₂ U X₂ ≤ 2 + X₂} OA= (X₁ ≤ 2 + X₂ U X₂ Z 2 + X₂} 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) =

customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X₁ and X₂ is as given in the accompanying table. x2 X1 0 1 2 3 4 0 1 2 3 0.07 0.04 0.00 0.09 0.05 0.15 0.05 0.04 0.05 0.04 0.10 0.06 0.00 0.03 0.04 0.07 0.00 0.02 0.05 0.05 (a) What is P(X₁ = 1, X₂= 1), that is, the probability that there is exactly one customer in each line? P(X₁ = 1, X₂= 1) = [ (b) What is P(X₁ = X₂), that is, the probability that the numbers of customers in the two lines are identical? P(X₁ = 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 X₁ and X₂- OA (X₁ 2 2 + X₂ U X₂ ≥ 2 + X₂} OA (X₁ ≤ 2 + X2₂ U X₂ ≤ 2 + X₂} OA (X₁ ≥ 2 + X₂ U X₂ ≤ 2 + X₂} OA= (X₁ ≤ 2 + X₂ U X₂ Z 2 + X₂} 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) =

MATLAB: An Introduction with Applications
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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A certain market has both an express checkout line and a superexpress 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 superexpress checkout at the same time. Suppose the joint pmf of X₁ and X₂ is as given in the accompanying table. X1 0 1 2 3 4 X2 3 0 1 2 0.09 0.07 0.04 0.00 0.05 0.15 0.05 0.04 0.05 0.04 0.10 0.06 0.00 0.03 0.04 0.07 0.00 0.02 0.05 0.05 (a) What is P(X₁ = 1, X₂ = 1), that is, the probability that there is exactly one customer in each line? P(X1 = 1, X₂ 1) = = (b) What is P(X₁ = X₂), that is, the probability that the numbers of customers in the two lines are identical? P(X1 = 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 X₁ and X₂. O A= {X₁ ≥ 2 + X₂ U X₂2 ≥ 2 + X₁} O A = {X₁ ≤ 2 + X₂ U X₂ ≤ 2 + X₁} O A = {X₁ ≥ 2 + X₂ U X₂ ≤ 2 + X₁} O A = {X₁ ≤ 2 + X₂ U X₂ ≥ 2 + X₁} 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) =
Transcribed Image Text:A certain market has both an express checkout line and a superexpress 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 superexpress checkout at the same time. Suppose the joint pmf of X₁ and X₂ is as given in the accompanying table. X1 0 1 2 3 4 X2 3 0 1 2 0.09 0.07 0.04 0.00 0.05 0.15 0.05 0.04 0.05 0.04 0.10 0.06 0.00 0.03 0.04 0.07 0.00 0.02 0.05 0.05 (a) What is P(X₁ = 1, X₂ = 1), that is, the probability that there is exactly one customer in each line? P(X1 = 1, X₂ 1) = = (b) What is P(X₁ = X₂), that is, the probability that the numbers of customers in the two lines are identical? P(X1 = 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 X₁ and X₂. O A= {X₁ ≥ 2 + X₂ U X₂2 ≥ 2 + X₁} O A = {X₁ ≤ 2 + X₂ U X₂ ≤ 2 + X₁} O A = {X₁ ≥ 2 + X₂ U X₂ ≤ 2 + X₁} O A = {X₁ ≤ 2 + X₂ U X₂ ≥ 2 + X₁} 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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