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# HW3 - b Verify that this is a valid probability...

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Stat 4714 HW 3 – Due Friday 9/10/2010 at 1:15pm (1) A certain federal agency employs three consulting firms (A, B, and C) with probabilities 0.40, 0.35, and 0.25 respectively. From past experience, it is known that the probabilities of cost overruns for the firms are 0.05, 0.03, and 0.15, respectively. a. Suppose a cost overrun is experienced by the agency. What is the probability that the consulting firm involved is company C? b. Suppose a cost overrun is experienced by the agency. What is the probability that the consulting firm involved is company A? (2) A shipment of 8 similar microcomputers to a retail outlet contains 3 that are defective. A school makes a random purchase of 2 of these microcomputers. a. Find the probability distribution for the number of defectives. (Note: You need to find the probabilities first.)

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Unformatted text preview: b. Verify that this is a valid probability distribution. c. Find the expected number and standard deviation of defective microcomputers. (3) Classify each of the following random variables as discrete or continuous: a. The number of automobile accidents per year in VA. b. The length of time to play 18 holes of golf. c. The amount of eggs laid each month by a hen. d. The weight of grain produced per acre. (4) Determine the value of c so that this function can serve as a probability distribution of the discrete random variable X. f(x) = c(x 2 +4) for x = 0, 1, 2, 3 (5) The probability distribution of X, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width, is given by X O 1 2 3 4 f(x) 0.41 0.37 0.16 0.05 0.01 Construct the cumulative distribution of X....
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