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# quiz7 - STA 4321/5325 Spring 2010 Quiz 7 April 2 Name There...

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Unformatted text preview: STA 4321/5325 - Spring 2010 Quiz 7 - April 2 Name: There are ﬁve problems in this quiz. Each problem has exactly one correct answer. Problem 1 The moment-generating function of a continuous random variable X with a probability density function f (x) is given by (a) ∞ −∞ xf (x)dx (b) ∞ 2 −∞ x f (x)dx (c) ∞x −∞ e f (x)dx (d) ∞ tx −∞ e f (x)dx Problem 2 Let MX (t) be the moment generating function of the random variable X . The k th (k ) dk derivative of MX (t) is given by MX (t) = dtk MX (t). Then the second moment of X be can calculated by (1) (a) MX (0) (b) V (X ) (2) (c) MX (0) (d) (E [X ])2 Problem 3 The moment-generating functions are unique; that is, two random variables that have the same moment-generating function have the same probability distributions as well. This statement is (a) True (b) False 1 Problem 4 Let X have a mixed distribution F (X ) writen uniquely as F (X ) = cF1 (X ) + (1 − c)F2 (X ) where F1 is the distribution function of a discrete random variable X1 and F2 is the distribution function of a continuous random variable X2 . Then E (X 2 ) is (a) cE (X1 ) + (1 − c)E (X2 ) (b) E (X1 ) + E (X2 ) 2 2 (c) cE (X1 ) + (1 − c)E (X2 ) 2 2 (d) E (X1 ) + E (X2 ) Problem 5 Let X has a gamma distribution with MX (t) = (1 − βt)−α . Then E (X ) is (a) α (b) αβ 2 (c) α2 β (d) αβ 2 ...
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quiz7 - STA 4321/5325 Spring 2010 Quiz 7 April 2 Name There...

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