14. -/5.88 points DevoreStat9 3.E.015 My Notes Ask Your Teacher Many manufacture

Question

14. -/5.88 points DevoreStat9 3.E.015 My Notes Ask Your Teacher 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 pairs (, 2) and (2, 1) represent the selection of boards 1 and 2 for inspection. (a) List the ten different possible outcomes. (Enter your answers as a comma-separated list of ordered pairs.) (b) Suppose that boards 2 and 5 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 p(x) (c) Let Fx) denote the cdf of X. First determine Fo) P(x s o), F1), and F(2); then obtain Fox) for all other x. F(x) = 2 5X Need Help? need" to a

Explanation / Answer

a)

Below are the list of possible outcomes

(1,2) (1,3) (1,4) (1,5) (2,3) (2,4) (2,5) (3,4) (3,5) (4,5)

b)

2 boards are defective

P(X = 0) = (2C0 * 3C2)/5C2 = 0.3

P(X = 1) = (2C1 * 3C1)/5C2 = 0.6

P(X = 2) = (2C2 * 3C0)/5C2 = 0.1

c)

F(x) = 0 , x < 0

= 0.3, 0 <= x < 1

= 0.6, 1 <= x < 2

= 0.1, 2 <= x

x 0 1 2 p(x) 0.3 0.6 0.1

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