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Practice Problems

Practice Problems. Actex 3, 4, 5. Section 3 -- #3. A box contains 4 red balls and 6 white balls. A sample of size 3 is drawn without replacement from the box. What is the probability of obtaining 1 red ball and 2 white balls, given that at least 2 of the balls in the sample are white ?

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Practice Problems

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  1. Practice Problems Actex 3, 4, 5

  2. Section 3 -- #3 A box contains 4 red balls and 6 white balls. A sample of size 3 is drawn without replacement from the box. What is the probability of obtaining 1 red ball and 2 white balls, given that at least 2 of the balls in the sample are white? Answer: 0.75

  3. Section 3 -- #6 An insurance company determines that N, the number of claims received in a week, is a random variable with P(N=n) = 1/2n+1, where n => 0. The company also determines that the number of claims received in a given week is independent of the number of claims received in any other week. Determine the probability that exactly seven claims will be received during a given two-week period. Answer: 1/64

  4. Section 4 -- #5 In a small metropolitan area, annual losses due to storm, fire, and theft are independently distributed random variables. The pdf’s are: Storm: f(x) = e-x Fire: f(x) = (2/3)e-2x/3 Theft: f(x) = (5/12)e-5x/12 Determine the probability that the maximum of these losses exceeds 3. Answer: 0.414

  5. Section 4 -- #10 • An insurance company insures a large number of homes. The insured value, X, of a randomly selected home is assumed to follow a distribution with density function, f(x)=3x-4 for x>1 and equal to zero otherwise. Given that a randomly selected home is insured for at least 1.5, what is the probability that it is insured for less than 2? Answer: 0.578

  6. Section 4 -- #16 The lifetime of a machine part has a continuous distribution on the interval (0, 40) with probability density function f, where f(x) is proportional to (10+x)-2. Calculate the probability that the lifetime of the machine part is less than 6. Answer: 0.46875

  7. Section 5 -- #7 A recent study indicates that the annual cost of maintaining and repairing a car in a town in Ontario averages 200 with a variance of 260. If a tax of 20% is introduced on all items associated with the maintenance and repair of cars (i.e. everything is made 20% more expensive), what will be the variance of the annual cost of maintaining and repairing a car? Answer: 374.4

  8. Section 5 -- #23 A random variable has the cumulative distribution function: F(x)= 0 for x < 1 (x2-2x+2)/2 for 1 <= x < 2 1 for x => 2 Calculate the variance of X. Answer: 5/36

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