A quality control plan calls for randomly selecting four items from the daily production (assumed large) of a certain machine and observing the number of defectives. The proportion p of defectives produced by the machine varies from day to day and has a uniform distribution on the interval(0,1).

Find the:

a. expected number of defectives observed among the three sampled items.
b. variance of the number of defectives among the three sampled.

A quality control plan calls for randomly selecting three items from the daily production (assumed large) of a certain machine and observing the number of defectives. However, the proportion p of defectives produced by the machine varies from day to day and is assumed to have a uniform distribution on the interval (O, 1). For a randomly chosen day, find the unconditional probability that exactly two defectives are observed in the sample.