Chapter 5.4, Problem 102E

Wasps. M. Goodisman et al. studied patterns in queen and worker wasps and published their findings in the article “Mating and Reproduction in the Wasp Vespula germanica” (Behavioral Ecology and Sociobiology, Vol. 51, No. 6, pp. 497–502). The number of male mates of a queen wasp has a Poisson distribution with parameter λ = 2.7. Find the probability that the number, Y, of male mates of a queen wasp is

1. a. exactly two.
2. b. at most two.
3. c. between one and three, inclusive.
4. d. On average, how many male mates does a queen wasp have?
5. e. Construct a table of probabilities for the random variable Y. Compute the probabilities until they are zero to three decimal places.
6. f. Draw a histogram of the probabilities in part (e).