Many manufacturers have quality control programs that include inspection of incomingmaterials for defects. Suppose a computer manufacturer receives circuit boards inbatches of five. Two boards are selected from each batch for inspection. We can representpossible 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 boardsare to be chosen at random. Define X to be the number of defective boards observedamong those inspected. Find the probability distribution of X.c. Let F(x) denote the cdf of X. First determine F(0) = P(X ≤ 0). F( 1). and F(2): thenobtain 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 ≤ 0). F( 1). and F(2): then
obtain F(x) for all other x.
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