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].

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Q: The joint probability mass function p(x,y) of X and Y is defined as follows: p(0,0)=0.5 p(1,0)=0.2…

A: Solution: From the given information, the probability mass function of X and Y is

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A: Solution

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A: the problem can be solved using the concept of expectation.

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Q: Exercise 20. Let X1 and X2 be iid U(0, 1) random variables. Find the joint probability density…

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