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 andof > 0. Suppose the covariance between X and Y is oxy and that ª ozy < ozo}. Thenthe conditional distribution of Y given X = x ER is the Gaussian distribution with meanα2222YOXY|Y|X=x = |y+ (x-µx).20²/12 Xand varianceof x = of - Xx2XY2X Q 7.2. Suppose X₁, X₂ and X3 have a joint Gaussian distribution with covariance matrix2 1 1(H)1 2 11 12find the conditional covariance of X₁ and X2 given X3.26x₁₁x₁1x₁ = 1/2/2X₂|X3

Covariance matrix is given To find conditional distribution of X1,X2 given X3Using the partition of…

Answered: Q 7.2. Suppose X₁, X2 and X3 have a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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For the following table of data. x 1 2 3 4 5 6 7 8 9 10 y 0 0.5 1 2 2.5 3 3 4 4.5 5 a. draw a scatterplot. b. calculate the correlation coefficient. c. calculate the least squares line and graph it on the scatterplot. d. predict the y value when x is 11.
The index model has been estimated for stocks A and B with the following results: RA = 0.03 + 0.8RM + eA. RB = 0.01 + 0.9RM + eB. σM = 0.35; σ(eA) = 0.20; σ(eB) = 0.10. The covariance between the returns on stocks A and B is A) 0384. B) 0.0406. C) 0.0882. D) 0.0772. E) 0.4000. 2) Analysts may use regression analysis to estimate the index model for a stock. When doing so, the slope of the regression line is an estimate of A) the α of the asset. B) the β of the asset. C) the σ of the asset. D) the δ of the asset. Choose correct answer with justification.
5.33 Refer to Exercise 5.27 and calculate the covariance between X and Y.
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Q2: (b) Let X₁, X2, X3 be uncorrelated random variables, having the same variance o². Consider the linear transformations Y₁ = X₁ + X₂, X2 + X3. Find the correlations of Y₁, Y; i, Y₂ = X₁ + X3 and Y3 for i + j. =

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Q 7.2. Suppose X₁, X2 and X3 have a joint Gaussian distribution with covariance matrix 2 1 1 1 2 1 1 2 find the conditional covariance of X₁ and X2 given X3. 6x₁x₁x₁ = = =