what is the expected value of x conditional on x? is it just x...?
If so does this then imply that var(x|x)=0 and cov(x,y|x)=0?
Are you trying to calculate E[X|X=x]? If not please clarify because a conditional probability needs a region for the B region given a P(A|B=c) or E[A|B=b] where b is some subset of the random variable b.
If x is fixed, then it means that E[X|X=x] = x and Var[X|x=x] = 0 since x has no variation.
On the other hand if x were the interval [0,1] then the answers would be different and you would calculate a conditional random variable and use that to get the expectation and variance.