Question: 22. Let X be the random variable that counts the number of events in each of the following cases. (a) The number of fish caught

22. Let X be the random variable that counts the number of events in each of the following cases.

(a) The number of fish caught by an angler in an afternoon.

(b) The number of disabled vehicles abandoned on I95 in a year.

(c) The number of wrongly dialed telephone numbers in a given city in an hour.

(d) The number of people who reach the age of 100 in a given city.

For each case explain how the Poisson approximation to the binomial distribution can be used to justify the use of the Poisson model for X, and discuss the assumptions that are needed for this justification.

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