Suppose that w has normal s2 distribution given that w w, Basic Statistics

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Suppose that w has normal s2 distribution given that w w

Question: Suppose that W has normal (µ, σ²) distribution. Given that W = w, suppose that Z has normal (α w + b, r²) distribution,

a) Show the joint distribution of W and Z is bivariate normal, and find its parameters.

b) What is the distribution of Z?

c) What is the conditional distribution of W given Z = z?

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Basic Statistics: Suppose that w has normal s2 distribution given that w w

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Basic Statistics: Suppose that w has normal s2 distribution given that w w

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