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In: Statistics and Probability

Suppose the number of customers arriving in a bookstore is Poisson distributed with a mean of...

Suppose the number of customers arriving in a bookstore is Poisson distributed with a mean of 2.3 per 12 minutes. The manager uses a robot to observe the customers coming to the bookstore. a)What is the mean and variance of the number of customers coming into the bookstore in 12 minutes? b)What is the probability that the robot observes 10 customers come into the bookstore in one hour? c)What is the probability that the robot observes at least one customer come into the bookstore within half an hour?

Suppose the time a customer spends in the bookstore is exponentially distributed with a mean of 8 minutes. d) Lisa arrives in the bookstore at 8:00 am, what is the probability that Lisa leaves between 8:04 and 8:05 am? e) Suppose the robot finds Lisa has been in the bookstore for 5 minutes and Jimmy has been in the bookstore for 6 minutes. Conditioned on that, what is the probability that Jimmy leaves the bookstore before Lisa? f) Suppose the robot has been observing the customers in the bookstore for one year, and finds that 50% of the customers will stay in the bookstore for k minutes. What is the value of k?

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orchestra answered 2 years ago
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