A quality control engineer believes that the proportion of defective items in a production process is a random variable with a probability distribution that is approximated as follows:
|
x
0.1
|
P (x)
0.1
|
|
0.2
|
0.3
|
|
0.3
|
0.2
|
|
0.4
|
0.2
|
|
0.5
|
0.1
|
|
0.6
|
0.1
|
The engineer collects a random sample of items and ?nds that 5 out of the 16 items in the sample are defective. Find the engineer's posterior probability distribution of the proportion of defective items.