10.3 The Russian mathematician Ladislaus Bortkiewicz noted that the Poisson dis- tribution would apply to low frequency events in a large population. even when the probabilities for individuals in the population 1varied. In a famous example he showed that the number of deaths by horse kick per year in the cavalry corps of the Prussian arm}.r follows the Poisson distribution. The following data is reproduced from Hoel (I934). y {deaths} 0 l 2 3 4 My] (frequency) 109 65 22 3 I (a) Suppose a prior uniform distribution is used for u. i. Find the posterior distribution for u. ii. What are the posterior mean. median, and variance in this case? (b) Suppose Jeffreys' prior is used for u. i. Find the posterior distribution for u. ii. What are the posterior mean. median. and variance in this case