Proposition 5.5 (Equation for the regression line). Suppose X and Y have a joint distribu- tion which is Gaussian, with the means and variances of X and Y being µx, µy, of >0 and o} > 0. Suppose the covariance between X and Y is oxy and that ª ozy < ozo}. Then the conditional distribution of Y given X = x ER is the Gaussian distribution with mean α 2 2 2 2 Y OXY |Y|X=x = |y+ (x-µx) .2 0²/12 X and variance of x = of - Xx 2 XY 2 X Q 7.2. Suppose X₁, X₂ and X3 have a joint Gaussian distribution with covariance matrix 2 1 1 (H) 1 2 1 1 12 find the conditional covariance of X₁ and X2 given X3. 2 6x₁₁x₁1x₁ = 1/2/2 | ×3
Proposition 5.5 (Equation for the regression line). Suppose X and Y have a joint distribu- tion which is Gaussian, with the means and variances of X and Y being µx, µy, of >0 and o} > 0. Suppose the covariance between X and Y is oxy and that ª ozy < ozo}. Then the conditional distribution of Y given X = x ER is the Gaussian distribution with mean α 2 2 2 2 Y OXY |Y|X=x = |y+ (x-µx) .2 0²/12 X and variance of x = of - Xx 2 XY 2 X Q 7.2. Suppose X₁, X₂ and X3 have a joint Gaussian distribution with covariance matrix 2 1 1 (H) 1 2 1 1 12 find the conditional covariance of X₁ and X2 given X3. 2 6x₁₁x₁1x₁ = 1/2/2 | ×3
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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why the answer is 0.5? could u please give me the detail? p2 includes the formulae you may need
Transcribed Image Text:Proposition 5.5 (Equation for the regression line). Suppose X and Y have a joint distribu-
tion which is Gaussian, with the means and variances of X and Y being µx, µy, of >0 and
o} > 0. Suppose the covariance between X and Y is oxy and that ª ozy < ozo}. Then
the conditional distribution of Y given X = x ER is the Gaussian distribution with mean
α
2
2
2
2
Y
OXY
|Y|X=x = |y+ (x-µx)
.2
0²/12 X
and variance
of x = of - Xx
2
XY
2
X
Transcribed Image Text:Q 7.2. Suppose X₁, X₂ and X3 have a joint Gaussian distribution with covariance matrix
2 1 1
(H)
1 2 1
1 12
find the conditional covariance of X₁ and X2 given X3.
2
6x₁₁x₁1x₁ = 1/2/2
| ×3
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