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# quiz3BS-f07 - ECON 506-M(solution NAME Quiz3-B 1 X and Y...

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ECON 506-M (solution) Quiz3-B, 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 Y. g(y) = dx x y 1 3 = 1.5(1-y 2 ) for 0<y< 1 = 0 elsewhere b. [10] Find the conditional distribution of (X | Y = 0.6) h (X|Y = 0.6) = [3x / 1.5(1-y 2 ] (for y= 0.6) = 3.125 x for 0.6<x<1 = 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 λ Poisson W , ) ( ~ 2 2 λ Poisson W and the two random variables are independent. Use MGF method to find the mass function for 2 1 W W W + = . ) 1 )( ( ) 1 ( ) 1 ( 2 1 2 1 2 1 ) ( * ) ( ) ( - + - - = = = t t t e e e W W W e e e t M t M t M λ λ λ λ ) ( ~ 2 1 λ λ + Poisson 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 found to be 10,000.

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