Suppose that a customer arrives at a checkout counter in a store just as the counter is opening.- A random number of customers N will be ahead of him, because some customers may arrive early. Suppose that this number has the probability distribution p(n) = P(N = n) = pq^n. n = 0, 1, 2,... where 0

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1)Suppose that a customer arrives at a checkout counter in a store just as the counter is opening.- A random number of customers N will be ahead of him, because some customers may arrive early. Suppose that this number has the probability distribution p(n) = P(N = n) = pq^n. n = 0, 1, 2,... where 0 <p < 1 and q = 1-p (this is a form of the geometric distribution). Customer service times are assumed to be independent and identically distributed exponential random variables with a mean of 0. For a given n, find the waiting time W for the customer to complete his checkout b Find the distribution of waiting time for the customer to complete his checkout. 2) Find the mean and the variance of the waiting time for the custome complete his checkout.

1)Suppose that a customer arrives at a checkout counter in a store just as the counter is opening.- A random number of customers N will be ahead of him, because some customers may arrive early. Suppose that this number has the probability distribution p(n) = P(N = n) = pq^n. n = 0, 1, 2,... where 0 <p < 1 and q = 1-p (this is a form of the geometric distribution). Customer service times are assumed to be independent and identically distributed exponential random variables with a mean of 0. For a given n, find the waiting time W for the customer to complete his checkout b Find the distribution of waiting time for the customer to complete his checkout. 2) Find the mean and the variance of the waiting time for the custome complete his checkout.

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1)Suppose that a customer arrives at a checkout counter in a store just as the counter is opening.- A random number of customers N will be ahead of him, because some customers may arrive early. Suppose that this number has the probability distribution

p(n) = P(N = n) = pq^n. n = 0, 1, 2,...

where 0 <p < 1 and q = 1-p (this is a form of the geometric distribution). Customer service times are assumed to be independent and identically distributed exponential random variables with a mean of 0. For a given n, find the waiting time W for the customer to complete his checkout b Find the distribution of waiting time for the customer to complete his checkout. 

2) Find the mean and the variance of the waiting time for the custome complete his checkout. 

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