# quiz5 - = R ∞(1-F X x dx This statement is(a True(b False...

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STA 4321/5325 Spring 2010 Quiz 5 March 3 Name: All problems have exactly one correct answer. Problem 1 Let X be a continuous random variable which takes non-negative values. Let f X denote the probability density function of X . Then (a) f X ( x ) = 0 for every x < 0. (b) f X ( x ) = 1 for every x < 0. (c) f X ( x ) < 0 for every x < 0. (d) f X ( x ) = 0 . 4 for every x < 0. Problem 2 Let X be a continuous random variable with probability density function f X and probability distribution function F X . Then for each x R , (a) F X ( x ) = R x -∞ f X ( y ) dy . (b) F X ( x ) = f 2 X ( x ). (c) F X ( x ) = d dx f X ( x ). (d) F X ( x ) = 1 f X ( x ) . Problem 3 If X is a continuous random variable taking non-negative values, then E ( X

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Unformatted text preview: ) = R ∞ (1-F X ( x )) dx . This statement is (a) True. (b) False. Problem 4 Let X be the uniform random variable on the interval [530 , 550]. Then (a) E ( X ) = 530. (b) E ( X ) = 550. (c) E ( X ) = 540. (d) E ( X ) = 350. 1 Problem 5 Let X be an exponential random variable with parameter 5. Then (a) P ( X ≤ 4) = e-4 5 . (b) P ( X ≤ 4) = 1-e-4 5 . (c) P ( X ≤ 4) = 1 5 e-4 5 . (d) P ( X ≤ 4) = 1 5 (1-e-4 5 ). Note that you have to compute P ( X ≤ 4), and not P ( X ≥ 4). 2...
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## This note was uploaded on 12/15/2011 for the course STA 4321 taught by Professor Staff during the Spring '08 term at University of Florida.

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quiz5 - = R ∞(1-F X x dx This statement is(a True(b False...

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