quiz3AS-f07 - ECON 506-M(solution NAME Quiz3-A 1 X and Y...

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ECON 506-M (solution) Quiz3-A, November 13, 2007 NAME: 1. X and Y have a joint bivariate distribution. f(x,y) = 3x if 0 < y < x < 1 0 otherwise. For a and b below, state the distribution, state the limits, and draw a small chart of the distribution. a. [8] Find the marginal distribution of X. g(x) = dy x x 0 3 = 3x 2 for 0<x< 1 = 0 elsewhere b. [10] Find the conditional distribution of (Y | X = 0.6) h (Y|X = 0.6) = [3x / 3x 2 ] (for x= 0.6) = 1.66 for 0<y<x = 0 elsewhere c. [12] Find E(XY) E(XY) = 3 . 0 ) 2 . 0 5 . 0 ) ( 3 ) 3 ( 1 0 5 2 1 0 4 1 0 1 2 1 0 1 = - = - = = ∫∫ ∫∫ y y dy y y ydxdy x dxdy x xy y y 2. [10] Let ) , ( ~ 1 1 p n Bin W , ) , ( ~ 2 2 p n Bin W and the two random variables are independent. Use MGF method to find the mass function for 2 1 W W W + = . 2 1 * ) 1 ( 1 * ) ( * ) ( ) ( 2 1 n n t t W W W e p e p t M t M t M + - - = = ) , ( ~ 2 1 p n n Bin W + 3. An economist is examining individual incomes in her country where it is assumed that incomes are normally distributed. The variance of individual income in the population is
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quiz3AS-f07 - ECON 506-M(solution NAME Quiz3-A 1 X and Y...

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