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Chapter 7: Q.28 (page 361)
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The number of accidents that a person has in a given year is a Poisson random variable with mean ̣ However, suppose that the value of changes from person to person, being equal to for percent of the population and for the other percent. If a person is chosen at random, what is the probability that he will have
(a) accidents and,
(b) Exactly accidents in a certain year? What is the conditional probability that he will have accidents in a given year, given that he had no accidents the preceding year?
Let be independent and identically distributed positive random variables. For find
For a group of 100 people, compute
(a) the expected number of days of the year that are birthdays of exactly 3 people;
(b) the expected number of distinct birthdays.
Ten hunters are waiting for ducks to fly by. When a flock of ducks flies overhead, the hunters fire at the same time, but each chooses his target at random, independently of the others. If each hunter independently hits his target with probability ., compute the expected number of ducks that are hit. Assume that the number of ducks in a flock is a Poisson random variable with mean .
Let have moment generating function , and define. Show that.
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