Question: For problem, suppose the biologists believed the proportion of infected crabs in the population was equally likely to be anywhere from 10% to 90%. Using the discrete points 0.1, 0.2, etc., construct a uniform prior distribution for the proportion of infected crabs, and compute the posterior distribution after the results of the sampling in problem.
Problem: An article in Forbes discusses the problem of oil and gas reserves around the world. Forecasting the amount of oil available is difficult. If the average number of barrels that can be pumped daily from an oil field is a normal random variable with mean 7,200 barrels and standard deviation 505 barrels, and a random sample of 20 days reveals a sample average of 6,100 barrels and standard deviation of 800, give a 95% highest-posterior-density credible set for the average number of barrels that can be pumped daily.