Recent years have seen a sharp decline in the Alaska king crab ?shery. One problem identi?ed 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 popula- tion. A ?sheries management agency monitoring crab catches needed to estimate the proportion of the adult crab population infected by the parasite. The agency's biolo- gists constructed the following prior probability distribution for the proportion of infected adult crabs (denoted by R):
|
R
0.25
|
P(R )
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.