The question is attached below

Let random variable Z have PDF f(z). Define the random variable Y = Z. In the followings provide complete derivations and explanations of results. The results should be given in terms of the PDF f (z). a) Find an expression for E[YIZ]. b) Find an expression for E[Z |Y]. c) Find an expression for Var (Y|Z). d) Find an expression for Var(Z|Y). e) Find the conditional CDF of Z given Y, and sketch it including all details. f) What type of random variable is Z conditioned on Y? If it is continuous, please indicate its PDF. If it is discrete then indicate its PMF