N(u, E) be a Gaussian random variable with mean u E Rd and covariance matrix E e Rdxd.Assuming that E is invertible. Let a e Rd be a fixed vector, and Y = a'X € R be a random variable.Calculate E[Y], Var(Y), E[X|Y = y], and Cov(X|Y = y) = E[Xx'|Y = y] – E[X|Y = y]E[X"|Y = y].Let X

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Answered: Let X ~ N(u, £) be a Gaussian random…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Let X ~ N(u, £) be a Gaussian random variable with mean u e Rd and covariance matrix E e Rdxd. Assuming that E is invertible. Let a e Rd be a fixed vector, and Y = aTX € R be a random variable. Calculate E[Y], Var(Y), E[X|Y = y), and Cov(X|Y = y) = E[Xx™|Y = y] – E[X|Y = y]E[X™|Y = y].