Many manufacturers have quality control programs that includeinspection of incoming materials for defects. Suppose a computermanufacturer receives circuit boards in batches of five. Two boards areselected from each batch for inspection. We can represent possibleoutcomes of the selection process by pairs. For example, the pair (1, 2)represents the selection of boards 1 and 2 for inspection. a. List the ten different possible outcomes.b. Suppose that boards 1 and 2 are the only defective boards in abatch. Two boards are to be chosen at random. Define X to be thenumber of defective boards observed among those inspected. Findthe probability distribution of X.c. Let F(x) denote the cdf of X. First determine F(0) = P(X≤O). F( 1).and F(2): then obtain F(x) for all other x.
Many manufacturers have quality control programs that include
inspection of incoming materials for defects. Suppose a computer
manufacturer receives circuit boards in batches of five. Two boards are
selected from each batch for inspection. We can represent possible
outcomes of the selection process by pairs. For example, the pair (1, 2)
represents the selection of boards 1 and 2 for inspection.
a. List the ten different possible outcomes.
b. Suppose that boards 1 and 2 are the only defective boards in a
batch. Two boards are to be chosen at random. Define X to be the
number of defective boards observed among those inspected. Find
the probability distribution of X.
c. Let F(x) denote the cdf of X. First determine F(0) = P(X≤O). F( 1).
and F(2): then obtain F(x) for all other x.
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