Many manufacturers have quality control programs that include inspection of incoming materials for defects. suppose a computer manufacturer receives computer boards in batches of five. two boards are randomly selected from each batch for inspection. consider batches for which exactly two of the boards are defective; for convenience, number the defective boards as 1 and 2, and the nondefective boards as 3, 4, and 5. let x denote the number of defective boards among the two actually inspected, and determine the mass function of x. hint: one possible sample of size 2 consists of boards 1 and 2, another of boards 1 and 3, and so on. how many such samples are there, and what is the value of x for each sample?

Question

Mathematics

Campbell Shea

19 September, 06:56

Many manufacturers have quality control programs that include inspection of incoming materials for defects. suppose a computer manufacturer receives computer boards in batches of five. two boards are randomly selected from each batch for inspection. consider batches for which exactly two of the boards are defective; for convenience, number the defective boards as 1 and 2, and the nondefective boards as 3, 4, and 5. let x denote the number of defective boards among the two actually inspected, and determine the mass function of x. hint: one possible sample of size 2 consists of boards 1 and 2, another of boards 1 and 3, and so on. how many such samples are there, and what is the value of x for each sample?

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Paula Hayden · Answer 1

There are ten combihations of the 5 boards taken 2 at a time. The values of x for each combination are as follows:

(1,2), x = 2; (1, 3), x = 1; (1,4), x = 1; (1, 5), x = 1; (2, 3), x = 1; (2, 4), x = 1; (2, 5), x = 1; (3,4), x = 0; (3, 5), x = 0; (4, 5), x = 0.

The mass function of x can be expressed as follows:

P (x = 0) = 0.3.

P (x = 1) = 0.6.

P (x = 2) = 0.1