The Russian mathematician Ladislaus Bortkiewicz noted that the Poisson distribution would apply to low-frequency events in a large population, even when the probabilities for individuals in the population varied. In a famous example he showed that the number of deaths by horse kick per year in the cavalry corps of the Prussian army follows the Poisson distribution. The following data is reproduced from Hoel (1984).

(a) Suppose a prior uniform distribution is used for .
i. Find the posterior distribution for .

ii. What are the posterior mean, median, and variance in this case?
(b) Suppose Je reys' prior is used for .
i. Find the posterior distribution for .
ii. What are the posterior mean, median, and variance in this case?

Transcribed Image Text:

Y (deaths) 0 1 2 3 4 n(y) (frequency) 109 65 22 3 1