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Customers arrive at a shop according to a Poisson process with rate = 10 per hour. The amount of money that each customer spends in

Customers arrive at a shop according to a Poisson process with rate = 10 per hour. The amount of money that each customer spends in the store can be modeled as an exponentially distributed random variable with a mean of 5 dollars. Additionally, we can assume that the amount of money that each customer spends is independent of the spending of the other customers.

(a) Compute the probability that the first two customers combined spend more than 12 dollars.1

(b) The shop opens at 8am and closes at 5pm. Compute the expected amount of money that customers will spend at the store over the course of the day.

(c) Compute the variance of the amount of money that customers will spend at the store over the course of the day.

(d) Compute the probability that, over the course of the day, every customer spends at least 2 dollars.

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