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Unformatted text preview: IE 230 Seat # ________ Name _____________________ Please read these directions. Closed book and notes. 60 minutes. Covers through the normal distribution, Section 4.6 of Montgomery and Runger, fourth edition. Cover page and four pages of exam. Pages 8 and 12 of the Concise Notes. A normal-distribution cdf table. No calculator. No need to simplify beyond probability concepts. For example, unsimplified factorials, integrals, sums, and algebra receive full credit. Throughout, f denotes probability mass function or probability density function and F denotes cumulative distribution function. For one point of credit, write your name neatly on this cover page. Circle your family name. For one point of credit, write your name on each of pages 1 through 4. Score ___________________________ Exam #2, October 19, 2010 Schmeiser IE 230 — Probability & Statistics in Engineering I Name _______________________ Closed book and notes. 60 minutes. 1. Suppose that the random variable X has the discrete uniform distribution over the set {0, 1,..., 10} and that the random variable Y has the continuous uniform distribution over the set [0, 10]. (a) (3 pt) T F E( X ) = E( Y ). (b) (3 pts) T F V( X ) = V( Y ). (c) (3 pts) T F F X (5) = F Y (5). (d) (3 pts) T F f X (5) = f Y (5). 2. (from Montgomery and Runger, 3–113) In 1898 L. J. Bortkiewicz published a book entitled The Law of Small Numbers . He used data collected over twenty years to show that the number of soldiers killed by horse kicks each year in each corps in the Prussian cavalry followed a Poisson distribution with a mean of 0.61. (a) (7 pts) For a particular corps over one year, determine the value of the probability of more than one death. (b) (7 pts) For a particular corps over five years, determine the value of the probability of no death. Exam #2, October 19, 2010 Page 1 of 4 Schmeiser IE 230 — Probability & Statistics in Engineering I Name _______________________ 3. (from Montgomery and Runger, 4–61) The lifetime of a semiconductor laser at a constant power is normally distributed with a mean of 6000 hours and standard deviation of 500 hours. (a) (8 pts) Sketch the corresponding normal pdf. Label and scale both axes. (b) (8 pts) Determine the value of the probability that a randomly selected laser fails between 4000 and 5000 hours. Provide at least three digits of precision. (c) (8 pts) Let q denote the correct answer to Part (b). If three lasers are used in a product, and all have independent lifetimes, determine the value of the probability that all three lasers fail between 4000 and 5000 hours....
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