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 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. x₂ 0 1 3 2 0.07 0.04 0.00 0 1 0.08 0.05 0.05 0.15 0.05 0.04 0.03 0.10 0.06 X₁ 2 3 0.00 0.02 0.04 0.07 4 0.00 0.01 0.05 0.09 (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 X₁₂ and X₂. O A = {X, $2 + Xy UXy 2 2 + Xị} O A = {X₁ ≥ 2 + X₂ UX₂ ≥ 2 + X₂} O A = {X₂ ≥ 2 + X₂ UX₂ ≤ 2+Xq} O A = (X₁ ≤ 2 + X₂ UX₂ ≤ 2 + X₂} Calculate the probability of this event. P(A) =

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