A certain market has both an express checkout line and a super-express checkout

Question

A certain market has both an express checkout line and a super-express 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 X2 0 0.08 0.05 0.05 0.00 0.00 0.08 0.17 0.04 0.03 0.01 0.04 0.05 0.10 0.04 0.05 0.00 0.02 0.06 0.07 0.06 4 The difference between the number of customers in line at the express checkout and the number in line at the superexpress checkout is X1 X2. Calca difference 0.18 the expected

Explanation / Answer

X1 - X2 can be computed for each cell in the matrix as:

Multiplying these values with the probability in the corresponding cells and adding them up = -0.17

Answer = -0.17

X2 X1 0 1 2 3 0 0 1 2 3 1 -1 0 1 2 2 -2 -1 0 1 3 -3 -2 -1 0 4 -4 -3 -2 -1

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