Assume that the total number of claims an insurance company receives each day follows a Poisson distribution with parameter 1000. For each claim received, there is a probability of 0.2 that the company will not make a payment. (Hint: given the number of claims for a day, the number of payments follows a Binomial distribution.)
(a) What is the expected number of payments each day for this company?
(b) Find the standard deviation for the number of payments each day for this company.
