Mathematics, 06.05.2020 08:25 finnierunners2

1. We considered a quality control plan that calls for randomly selecting three 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 thea. expected number of defectives observed among the three sampled items. b. variance of the number of defectives among the three sampled.2. A quality control plan calls for randomly selecting nine 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). For a randomly chosen day, find the un-conditional probability that exactly two defectives are observed in the sample.

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