Answer the questions

10.4 The number of defects per 10 meters of cloth produced by a weaving machine has the Poisson distribution with mean u. You examine 100 meters of cloth produced by the machine and observe 71 defects. (a) Your prior belief about & is that it has mean 6 and standard deviation 2. Find a gamma(r, v) prior that matches your prior belief. (b) Find the posterior distribution of / given that you observed 71 defects in 100 meters of cloth. (c) Calculate a 95% Bayesian credible interval for u