# Question: The number of accidents that a person has in a

The number of accidents that a person has in a given year is a Poisson random variable with mean λ. However, suppose that the value of λ changes from person to person, being equal to 2 for 60 percent of the population and 3 for the other 40 percent. If a person is chosen at random, what is the probability that he will have (a) 0 accidents and (b) exactly 3 accidents in a certain year? What is the conditional probability that he will have 3 accidents in a given year, given that he had no accidents the preceding year?

## Answer to relevant Questions

Repeat Problem 68 when the proportion of the population having a value of λ less than x is equal to 1 − e−x. Problem 68 The number of accidents that a person has in a given year is a Poisson random variable with mean ...The moment generating function of X is given by MX(t) = exp{2et − 2} and that of Y by MY(t) = (3/4et + 1/4)10. If X and Y are independent, what are (a) P{X + Y = 2}? (b) P{XY = 0}? (c) E[XY]? A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her expected winnings. Let X(i), i = 1, . . . , n, denote the order statistics from a set of n uniform (0, 1) random variables, and note that the density function of X(i) is given by f(x) = n!/(i − 1)!(n − i)! xi−1(1 − x)n−i 0 < x < ...An urn contains a white and b black balls. After a ball is drawn, it is returned to the urn if it is white; but if it is black, it is replaced by a white ball from another urn. Let Mn denote the expected number of white ...Post your question