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A grocery store has both a regular checkout line and an express checkout line. Let 푋1be...

A grocery store has both a regular checkout line and an express checkout line. Let 푋1be the number of customers in the regular checkout line at a particulartime of day, and let 푋2be the number of customers in the express checkout lineat the same time. The joint PMF of 푋1and 푋2is given in the table below. 푋20123푋10.08.07.04.001.06.15.05.042.05.04.10.063.00.03.04.074.00.01.05.06(1) How do you know this is a valid PMF?(2) What is the probability that there areexactly two customers in each line?(3) What is the probability that the numbers of customers in the two lines are identical?(4) What is the probability that the total number of customers in the two lines is at least four?(5) What is the probability that the express line has no customer?(6) Given that there are at least two customers in the express line, what is the conditional probability that the regular line has no customer?

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