Suppose that Y is a normal random variable with mean and variance 2, and suppose also that the conditional distribution of X, given that Y y, is normal with mean y and variance 1 (a) Argue that the joint distribution of X, Y is the same as that of Y Z, Y when Z is a standard normal random variable ...

a This follows because the conditional distribution of ...

Suppose that Y is a normal random variable with mean and variance 2, and suppose also

Question:

Suppose that Y is a normal random variable with mean μ and variance σ2, and suppose also that the conditional of X, given that Y = y, is normal with mean y and variance 1.
(a) Argue that the joint of X, Y is the same as that of Y + Z, Y when Z is a standard normal random variable that is independent of Y.
(b) Use the result of part (a) to argue that X, Y has a bivariate normal Find E[X], Var(X), and Corr(X, Y).
(d) Find E[Y|X = x].
(e) What is the conditional of Y given that X = x? Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...