Let X and Y have a bivariate normal distribution with X 70, 2X 100, Y 80, 2Y 169, and 5 13 Find (a) E(Y X 72) (b) Var(Y X 72) (c) P(Y 84, X 72)

Question: Let X and Y have a bivariate normal distribution with X = 70, 2X = 100, Y = 80, 2Y = 169, and =

Let X and Y have a bivariate normal with μX = 70, σ2X = 100, μY = 80, σ2Y = 169, and ρ = 5/13. Find
(a) E(Y | X = 72).
(b) Var(Y| X = 72).
(c) P(Y ≤ 84, | X = 72).

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