2. A hospital in the United States wants to evaluate their success rate of heart transplant surgeries We observe the number of deaths, y, in a number of heart transplant surgeries. Let y N Pois(1/)\\) Where A is the rate of deaths / patient and V is the exposure (total number of heart transplant patients). When measuring rare events with low rates, maximum likelihood estimation can be notoriously bad. We'll tak a Bayesian approach. To construct your prior distribution you talk to two experts. The rst expert thinks that 13100 With a gamma(3, 2000)$ density is a reasonable prior. The second expert thinks that 19200 with a gamma(7, 1000) density is a reasonable prior distribution. You decide that each expert is equally credible so you combine their prior distributions into a mixture prior with equal weights: p()\\) : 0.5 >1: 1010') + 0.5 * p2(/\\) (a) What does each expert think the mean rate is, a priori? Which expert is more condent about the value of A a priori (i.e. before seeing any data)