Suppose that customers arriving at a 24-hour supermarket follow a Poisson process with rate λ = 10 per hour. Let Xi be the random variable denoting the amount spent by each arriving customer. Suppose that Xi ’s are independent and identically distributed with mean 100 AED and standard deviation 25 AED. Let us also assume that the number of customers arriving at the supermarket is independent of the amount spent by each customer. Let T be the total sales (amount spent by all the customers) at the supermarket on any single day. Find the expected value and variance of T. Using the Chebyshev inequality, find an upper bound on the probability that the daily sales at the supermarket will fall below 20,000 AED?
Suppose that customers arriving at a 24-hour supermarket follow a Poisson process with rate λ = 10 per hour. Let Xi be the random variable
denoting the amount spent by each arriving customer. Suppose that Xi ’s
are independent and identically distributed with
customer. Let T be the total sales (amount spent by all the customers)
at the supermarket on any single day. Find the
probability that the daily sales at the supermarket will fall below 20,000
AED?
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