A certain market has both on express checkout lire and a super express checkout

Question

A certain market has both on express checkout lire and a super express checkout line. Let x_1 denote the number of customers in line at the express checkout at a particular time of day, and let x_2 denote the number of customers in line at the super express checkout at the same time. Suppose the joint pmf of x_1 and x_2 is as given in the accompanying table. (a) What is rho(X_1 = 1, X_2 = 1), that is, the probability that there is exactly one customer in each line? rho (X_1 = 1, X_2 = 1) = 5 (b) What is P(X_1 = X_2), that is, the probability that the numbers of customers in the two liners are identical. rho (X_1 = X_2) = .4 (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_1 and X_2 A = (X_1 greaterthanorequalto 2 + X_2 X_2 greaterthanorequalto 2 + X_1) A = (X_1 lessthanorequalto 2 + X_2 lessthanorequalto 2 + X_1) a = (X_1 greaterthanorequalto 2 + X_2 X_2 lessthanorequalto 2 + X_1) A - (X_1 lessthanorequalto 2 + X_2 X_2 greaterthanorequalto 2 + X_1) Calculate the probability of this event. P(A) = -.23 (d) What is the probability that the total number of customers in the two lines is exactly four? At least four? P(exactly four) = 16 P(at least four) = .45

Explanation / Answer

from above table proabailty that number of customer in one line is 2 or more then in other line

=0.04+0.04+0.05+0.02+0.01=0.16

d) P(exactly 4) =P(1.3)+P(2,2)+P(3,1)+P(4,0) =0.04+0.10+0.02+0.00=0.16

P(at least 4) =0.00+0.02+0.01+0.1+0.04+0.05+0.04+0.06+0.04+0.11=0.47

please revert for doubt

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