410Hw07 - STAT 410 Homework #7 Summer 2009 (due Monday,...

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Unformatted text preview: STAT 410 Homework #7 Summer 2009 (due Monday, July 20, by 4:00 p.m.) Warm-up: 4.2.3 1. a) 4.1.4 b) 4.1.8 a) 4.1.4 Let X 1 , X 2 , X 3 , X 4 be four iid random variables having the same pdf f ( x ) = 2 x , 0 < x < 1, zero elsewhere. Find the mean and variance of the sum Y of these four random variables. b) 4.1.8 Determine the mean and variance of the mean X of a random sample of size 9 from a distribution having pdf f ( x ) = 4 x 3 , 0 < x < 1, zero elsewhere. 2. a) 4.1.9 b) 4.1.13 a) 4.1.9 Let X and Y be random variables with 1 = 1, 2 = 4, 1 2 = 4, 2 2 = 6, = 2 1 . Find the mean and variance of Z = 3 X 2 Y. b) 4.1.13 Determine the correlation coefficient of the random variables X and Y if Var ( X ) = 4, Var ( Y ) = 2, and Var ( X + 2 Y ) = 15. 3. 4.1.22 + (c) Let X be N ( , 2 ) and consider the transformation X = ln ( Y ) or, equivalently, Y = e X . (a) Find the mean and the variance of Y by first determining E ( e X ) and E [ ( e X ) 2 ] , by using the mgf of X....
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410Hw07 - STAT 410 Homework #7 Summer 2009 (due Monday,...

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