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 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 Hoe] [1934). y (deaths) 0 l 2 3 4 niy) (frequency) \"39 65 22 3 l (a) Suppose a prior uniform distribution is used for p. i. Find the posterior distribution for #- 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 it. ii. What are the posterior mean. median. and variance in this case? 8.4 You are going to take a random sample of voters in a city in order to estimate the proportion it who support stopping the uoridation of the municipal water supply. Before you analyze the data. you need a prior distribution for 1r. You decide that your prior mean is .4. and your prior standard deviation is .l. (a) Determine the bera(o. h} prior that matches your prior belief. (b) What is the equivalent sample size of your prior? is) Out of the 100 city voters polled. y = 21 support the removal of u oridation from the municipal water supply. Determine your posterior distribution