quiz5 - STA 4321/5325 - Spring 2010 Quiz 5 - March 19 Name:...

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Unformatted text preview: STA 4321/5325 - Spring 2010 Quiz 5 - March 19 Name: There are five problems in this quiz. Each problem has 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) = 1 for every x < 0 (b) f (x) = 0 for every x < 0 (c) f (x) < 0 for every x < 0 (d) f (x) = 0.5 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) = d dx f (x) (b) F (x) = f 2 (x) (c) F (x) = (d) F (x) = x −∞ f (y )dy 1 f (x ) Problem 3 Let X be a continuous random variable taking non-negative values, then ∞ E (X ) = 0 (1 − F (x))dx. This statement is (a) True (b) False 1 Problem 4 Let X be the uniform random variable on the interval [530, 550]. Then (a) E (X ) = 530 (b) E (X ) = 540 (c) E (X ) = 550 (d) E (X ) = 20 Problem 5 Let X be the exponential random variable with parameter 5. Then 4 1 (a) P (X ≥ 4) = 5 (1 − e− 5 ) 4 (b) P (X ≥ 4) = 1 − e− 5 4 (c) P (X ≥ 4) = 1 e− 5 5 4 (d) P (X ≥ 4) = e− 5 Note that the density function of exponential random variable is f (x) = x 1 −β βe 0 2 , for x ≥ 0 , for x < 0 ...
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This note was uploaded on 06/05/2011 for the course STA 4321 taught by Professor Staff during the Spring '08 term at University of Florida.

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quiz5 - STA 4321/5325 - Spring 2010 Quiz 5 - March 19 Name:...

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