Spring 2011 Exam 3

# Spring 2011 Exam 3 - Probability and Statistics for...

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Probability and Statistics for Engineering (ESE 326) Exam 3 AprlI 14,20Il each, five true-false problems each, and two free-response This exam contains eight multiple-choice problems worth two points worth one point each, eight short-answer problems worth one point problems worth 11 points altogether, for an exam total of 40 points. Part I. Multiple-Choice (two points each) Clearly fill in the oval on your answer card which corresponds to the only correct response. 1. ArandomvariableXhasthefollowingdensityfunctionwithdunknown: f (*) -02re-0', r) 0. Let Xy. .. , Xn be a random sample of size n from the distribution of X. Find the maximum likelihood estimator for 9. 2. Suppose X is anormal random variable with pl:50 and o:3. Let X1,. ..,Xa be arandom sample of size n : 6 from the distribution of X. Find PIX > Sfl. (A) .0228 (B) .2071 (c) .2525 (D) .36e4 (E) .6306 (F) .7475 (G) .7e2e (H) .e772 (A) (B) (c) (D) (E) (F) (G) (H) 2x 2 X 2x n 2n X x 2 I 2X x 2n n 2X

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(A) (B) (c) (D) (E) (F) (G) (H) (D (r) 8 12 18 22 46 54 4. 5. 3. Let X andY be independent random variables with oa : 5 and oy : 2. Find ozx-y. t/46 Ja {e6 lLo4 Let X be a random variable, and suppose ["t1, L2] is a confidence interval for the mean p, of X, where a : .05. Which of the following is an appropriate statement to make about this interval? (A) We are 95% confident that p lies in this interval. (B) We are 95% confident that p lies outside this interval. (C) We are 95% confident that T lies in this interval. (D) We are 95% confident that 7lies outside this interval. (E) We are 95% confident that X lies in this interval. (F) We are 95% confident that X hes outside this interval. Suppose a random variable X is known to be normal with standard deviation o :12. What sample size is required to estimate pr to within 2 units of its true value withg2o/o confidence? (A) 10 (B) 11 (c) 27 (D) 28 (E) 35 (F) 36 (G) 7r (H) 72 (r) 110 (J) 111
6. Three distribution curves are shown below. Two of them are ? distributions, namely, Tr and T5, and the other is Z, the standard normal curve. Decide which must be which, and then put them in 1-2-3 order as shown. (A)

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Spring 2011 Exam 3 - Probability and Statistics for...

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