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 Y 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 super-express checkout at the same time. Suppose the joint probability mass function of Y and X is as given in the accompanying table.                         
                              X     p(x,y)    0       1        2       3      0       0.08   0.07   0.04 0      1        0.06   0.15   0.05   0.04 Y   2       0.05   0.04   0.1      0.06      3        0       0.03   0.04    0.07      4        0       0.01   0.05    0.06 a). What is the probability that the number of customers in the two lines are identical? b). You are interested in examining whether the express checkout handles more customers that the super-express checkout. Generate the probability mass function of the random variable A, where A=Y-X. c). What is the probability that the express checkout has more customers than the super-express checkout, that is, the p(A > 0). A certain market has both an express checkout line and a super-express checkout line. Let Y 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 super-express checkout at the same time. Suppose the joint probability mass function of Y and X is as given in the accompanying table.                         
                              X     p(x,y)    0       1        2       3      0       0.08   0.07   0.04 0      1        0.06   0.15   0.05   0.04 Y   2       0.05   0.04   0.1      0.06      3        0       0.03   0.04    0.07      4        0       0.01   0.05    0.06 a). What is the probability that the number of customers in the two lines are identical? b). You are interested in examining whether the express checkout handles more customers that the super-express checkout. Generate the probability mass function of the random variable A, where A=Y-X. c). What is the probability that the express checkout has more customers than the super-express checkout, that is, the p(A > 0).

Explanation / Answer

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