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# LQ3B - I E 27 Third Long Quiz(THV THW 2008 August 16(1:00...

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2008 August 16 (1:00 PM – 4:00 PM) General Instructions: 1. You may use only pens with Black or Blue ink; otherwise only 50% of score is recorded. 2. Students caught cheating will automatically get a grade of 5.0 in this course. 3. Do not round off intermediate values. Final answers should be given in exactly 5 significant digits. 4. Box final answers. Should there be ambiguity on what your final answer is, you stand to lose all the points in that item. 5. Late papers will receive a 1-point penalty for every minute late. 6. Use of cell phones is prohibited. 7. Use only the right side of your bluebook. Use the left side for scratch. The teacher will not check stuff written on the left side of the bluebook. 8. No borrowing of calculators between students. In case two students are caught sharing a calculator, teacher will keep said calculator for the duration of the test. 9. Insert questionnaire in bluebook after the test. Bluebooks with no questionnaires inserted will not be checked. Highest possible score: 121/120 (101%) Passing: 71/120 (60%) I. Possible or Impossible . If the descriptions provided could not possibly occur within the rules governing probability distributions or mathematical laws in general, mark the item Impossible. Otherwise, mark it Possible. (20 points - 2 points each) 1. A random variable with pdf, f(x) = x for 0 < x < 2 (0 otherwise). 2. A random variable with cdf, F(x) = 1 for 5 < x < 10 (0 otherwise). 3. A random variable with pdf f(x) = e x for x 0 (0 otherwise). 4. A random variable with cdf defined as follows:

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5. A random variable with pdf defined as follows: 6. A gamma random variable, X, with 7. A normally distributed random variable with standard deviation of 0. 8. A uniformly distributed continuous random variable, X, with 9. Positive numbers a and b such that a < b and Γ (a) > Γ (b). 10. A value for k such that P(X < k) = 0 for the lognormal random variable X. II. True or False . If the statements provided are necessarily true, mark the item True. Otherwise, mark it False. (11 points - 1 point each) 1. The Central Limit Theorem guarantees that if we take enough observations of a random variable X, the distribution of the variable will approach the shape of the normal distribution. 2. The Central Limit Theorem applies only to continuous random
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LQ3B - I E 27 Third Long Quiz(THV THW 2008 August 16(1:00...

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