A quality control plan for an assembly line involves sampling n = 10 finished items
per day and counting Y , the number of defectives. If p denotes the probability of
observing a defective, then Y has a binomial distribution, assuming that a large number
of items are produced by the line. But p varies from day to day and is assumed to have
a uniform distribution on the interval from 0 to 1/4. Find the expected value of Y .