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stat400lec28
Course: STAT 400, Fall 2008School: University of Illinois,...
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Statistics 400 Section 5.6 <a href="/keyword/bivariate-normal/" >bivariate normal</a> distribution Two random variables X and Y have a <a href="/keyword/bivariate-normal/" >bivariate normal</a> distribution with 2 means X and Y , variances X and Y2 , correlation coefficient . 2 X X X ~ , N Y Y X Y X Y 2 Y They have a...
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Statistics 400 Section 5.6 <a href="/keyword/bivariate-normal/" >bivariate normal</a> distribution Two random variables X and Y have a <a href="/keyword/bivariate-normal/" >bivariate normal</a> distribution with 2 means X and Y , variances X and Y2 , correlation coefficient . 2 X X X ~ , N Y Y X Y X Y 2 Y They have a joint pdf f ( x, y ) = 1 2 X Y - X - X y - Y 1 x x exp[- [ - 2 2(1 - 2 ) X X Y 1- 2 2 y - Y + ]] Y 2 The conditional pdf of Y given X=x is normal distribution Ping Ma Lecture 28 -1- Y | X = x ~ N ( Y + That is Y 2 ( x - X ), (1 - 2 ) Y ) X E[Y | X = x] = Y + Y (x - X ) X Var[Y | X = x] = (1 - 2 ) Y2 (1) conditional distribution is also normal (2) E(Y|X=x) is a linear function of x (3) Var(Y|X=x) does not depend on the value of x. Ping Ma Lecture 28 -2- Example Two random variables X and Y have a <a href="/keyword/bivariate-normal/" &g...
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