Question

In 1989, Ladislaus Bortkiewicz published a book titled The Law of Small Numbers. He used data collected over 20 years to show that the number of soldiers killed by horse kicks in each corps in the Prussian cavalry is a Poisson process with rate α = 0.61 per year. (a) (3 points) If we can expect 0.61 horsekick related deaths per year, as specified in the problem, how many horse kick related deaths would you expect over a two-year period in a Prussian cavalry corp? (b) (1 point) Since the number of soldiers killed by horse kicks in a Prussian cavalry corp can be modeled using Poisson process, the number of horse kick related deaths over a two-year period (and any other time intervals) is a Poisson random variable. Define X = the number of soldiers killed by horse kicks in a Prussian cavalry corp over a two-year period. Then, we can say that X ∼ Poi(μ = ). (c) (6 points) Find the probability that at most one soldier would die due to horse kicks in a Prussian cavalry corps over a two-year period using the random variable defined in Part (b).

Answer 1