We provide an alternative proof of the conditional density of the normal dis-tribution. Let X₁, X₂ € R be such that0²102(X₂)~ N((~) . (₂))102i.e. the vector X is bivariate normal.i) Find a E R such thatCov(X₁ - aX2, X₂) = 0 .What does this imply about the random variables Y = X₁ - aX₂ and X₂?ii) By writing X₁ in terms of Y and X2, rederive the conditional distribution of X₁ |X₂ =x2.

From the given information, EX1=μ1EX2=μ2VX1=σ12VX2=σ22CovX1,X2=ρσ1σ2 i) Consider,…

Answered: We provide an alternative proof of the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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We provide an alternative proof of the conditional density of the normal dis- tribution. Let X₁, X2 E R be such that (X₁) ~ N((11), (01 102 00102)), i.e. the vector X is bivariate normal. i) Find a E R such that