Question: Recent years have seen a sharp decline in the Alaska king crab fishery. One problem identified as a potential cause of the decline has been the prevalence of a deadly parasite believed to infect a large proportion of the adult king crab population. A fisheries management agency monitoring crab catches needed to estimate the proportion of the adult crab population infected by the parasite. The agency's biologists constructed the following prior probability distribution for the proportion of infected adult crabs (denoted by R):
R P(R)
0.25 0.1
0.30 0.2
0.35 0.2
0.40 0.3
0.45 0.1
0.50 0.1
A random sample of 10 adult king crabs was collected, and 3 of them were found to be infected with the parasite. Construct the posterior probability distribution of the proportion of infected adult crabs, and plot it.