I think your missing somewhere.
What you have here, is variance of something equal to zero, hence it's a constant.
Are you trying to show that the MSE = Bias squared + variance?
BUT the problem here is understanding what a statistic is and what a parameter is.
A parameter is NOT a function of the data, X. A statistic is a function of X.
http://www.mathhelpforum.com/math-he...ror-proof.html