hw4s - BIVARIATE NORMAL UIN = 443 34 8339 EX= 9 Marginal...

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MSPE PROGRAM ECON 506 FALL 2011 SOLUTION TO HW 4 Part C: P(x,y) y 2 5 8 P(x) x 1 0.10 0.10 0.10 0.30 3 0.00 0.20 0.20 0.40 5 0.00 0.00 0.30 0.30 P(y) 0.10 0.30 0.60 1.00 x P(x) XP(X) X^2P(X) y P(Y) YP(Y) Y^2P(Y) X Y XY P(X,Y) XYP(X,Y) 1 0.300 0.3 0.3 2 0.100 0.2 0.4 1 2 2 0.1 0.2 3 0.400 1.2 3.6 5 0.300 1.5 7.5 3 2 6 0.0 0 5 0.300 1.5 7.5 8 0.600 4.8 38.4 5 2 10 0.0 0 1 5 5 0.1 0.5 E(X)= 3.000 E(Y)= 6.5 3 5 15 0.2 3 E(X^2)= 11.4 E(Y^2)= 46.3 5 5 25 0.0 0 VAR(X)= 2.4 VAR(Y)= 4.05 1 8 8 0.1 0.8 STD(X)= 1.549 STD(Y)= 2.012 3 8 24 0.2 4.8 5 8 40 0.3 12 COV(X,Y)= 1.8 E(XY)= 21.3 CORR(X,Y)= 0.577 Part D:
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Unformatted text preview: BIVARIATE NORMAL UIN = 443 34 8339 EX= 9 Marginal pdf of Y is Normal with mean 3 and variance 5 EY= 3 V(X)= 10 Conditional pdf of Y given X=3 is Normal with mean= V(Y)= 5 and variance= 2.5 COV(X,Y)= 5 Conditional pdf of X given Y=-2 is Normal with mean= 4 STD(X)= 3.1622777 and variance= 5 STD(Y)= 2.236068 corr(X,Y)= 0.7071068...
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