Question: Let X and Y be jointly normal random variables with parameters X = 2, 2 X = 4, Y = 1,

Let X and Y be jointly normal random variables with parameters μX = 2, σ2X = 4, μY = 1, σ2Y = 9, and ρ = −1/2.

a. Find E[Y |X = 3].

b. Find V ar(Y |X = 2).

c. Find P(X +2Y ≤ 5|X +Y = 3).

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