Question: Suppose that Y|X = x N(5 2x, 16), that is, given X = x, Y has the normal distribution with mean Y|X(x) =

Suppose that Y|X = x ∼ N(5 − 2x, 16), that is, given X = x, Y has the normal distribution with mean μY|X(x) = 5 − 2x and variance σ2

ε = 16, and let σX = 3.

(a) Find σ2Y and ρX,Y.

(b) If Y1 is an observation to be taken when X has been observed to take the value 1, find the 95th percentile of Y1.

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