The number of accidents that a person has in a given year is a poisson random variable with mean λ. however, we may suppose that the rate λ depends on the person or portion of the population. suppose that λ=3 for 65 percent of the population, and λ=4 for the other 35 percent.
(a) if a person is chosen at random, what is the probability that s/he will have zero accidents in a certain year? p(no accidents)=
(b) if a person is chosen at random, what is the probability that s/he will have 5 accidents in a certain year?
p(5 accidents)=
(c) what is the conditional probability that the person will have 5 accidents in a given year, given that s/he had none in the preceding year?
p(5 accidents|none preceding)=