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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 4.7 of Montgomery and Runger, fourth edition. Cover page and four pages of exam. Page 8 of the Concise Notes. 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. A true-or-false statement is true only if it always true; any counter-example makes it false. For one point, write your name neatly on this cover page and circle your family name. Score ___________________________ Exam #2, March 8, 2011 Schmeiser IE 230 — Probability & Statistics in Engineering I Name _______________________ Closed book and notes. 60 minutes. For statements a—g, choose true or false, or leave blank. (three points if correct, one point if left blank, zero points if incorrect) (a) T F The continuous-uniform family of distributions is a special case of the discrete-uniform family. (b) T F Scheduled arrivals, such as to physician’s office, are naturally modeled with a Poisson process. (c) T F Consider a discrete random variable X with probability mass function f X . Then ∫ −∞ ∞ f X ( c ) dc = 1. (d) T F Consider a random variable X with Poisson distribution with mean μ = 3 arrivals. Because σ X 2 = μ , the units of σ X are arrivals 1 / 2 . (e) T F If Z is a standard-normal random variable, then P( Z = 0) = 0. (f) T F If Z is a standard-normal random variable, then f Z (0) = 0, where f Z is the probability density function of Z . (g) T F If Z is a standard-normal random variable, then F Z ( − 3.2) = F Z (3.2), where F Z is the cdf of Z . 2. Suppose that the random variable X has the discrete uniform distribution over the set {1, 2,..., 10} and that the random variable Y has the continuous uniform distribution over the set [1, 10]. For statements a–e, choose true or false. (a) (3 points) T F E( X ) = E( Y ). (b) (3 points) T F V( X ) = V( Y ). (c) (3 points) T F F X (5.5) = F Y (5). (d) (3 points) T F f X (5.5) = f Y (5). (e) (3 points) T F P( X = 5) = f X (5). Exam #2, March 8, 2011 Page 1 of 4 Schmeiser IE 230 — Probability & Statistics in Engineering I Name _______________________ 3. (from Montgomery and Runger, 4–50) The time until recharge for a battery in a laptop computer under common conditions is normally distributed with mean 260 minutes and a standard deviation of 50 minutes....
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