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Unformatted text preview: AMS 310: Survey of Probability and Statistics MIDTERM EXAM I Spring 2009 Last Name: First Name: ID: Show all your work for full credit 1. Given a set of observations: 12 30 30 27 30 39 18 27 48 24 18 (a) (5pts) Find the 90th percentile. (b) (5pts) Find the minimum, maximum, range, and the interquartile range. (c) (5pts) Draw a boxplot. 2. Let X be a discrete random variable taking values in { 3 , , 3 , 6 } with probability mass function P ( X = 3) = 1 4 ,P ( X = 0) = 1 3 ,P ( X = 3) = 1 4 ,P ( X = 6) = 1 6 . (a) (6pts) Compute the mean E ( X ), variance V ar ( X ), and standard deviation of X . (b) (6pts) Calculate the probabilities P ( X ≤  2), P ( X ≤ 3), and P ( X ≤ 6 . 2). 1 3. Suppose that P ( E ) = 0 . 6. What can you say about P ( E  F ) under the following cases: (a) (5pts) E and F are mutually exclusive? (b) (5pts) E and F are independent? (c) (5pts) E ⊂ F ? (d) (5pts) F ⊂ E ?...
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 Spring '08
 Mendell
 Probability, Standard Deviation, Probability distribution, Probability theory, Probability mass function

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