Suppose that a random variable X has a normal distribution, and for every x, the conditional distribution of another random variable Y given that X x is a normal distribution with mean ax b and variance 2, where a, b, and 2 are constants Prove that the joint distribution of X and Y is a bivariate normal distribution

Question: Suppose that a random variable X has a normal distribution, and for every x, the conditional distribution of another random variable Y given that X

Suppose that a random variable X has a normal and for every x, the conditional of another random variable Y given that X = x is a normal with mean ax + b and variance τ2, where a, b, and τ2 are constants. Prove that the joint of X and Y is a bivariate normal

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