You wish to measure random variable X with expected value EIX] = 1 and variance Var[X] = 1, but your measurement procedure yields the noisy observation Y = X + Z, where Z is the Gaussian (0,2) noise that is independent of X.
(a) Find the conditional PDF fZ|X(z|x) of Z given X = x.
(b) Find the conditional PDF fY|X(y|2) of Y given X = 2. Given X = x, Y = x + Z.