I guess this is not a difficult problem, but I can not find the function for which to use Chebyshev's inequality...
Assume X is a random variable with property that . Use Chebyshev's inequality for the random variable to prove that for .
You have, using Chebyshev's inequality, for , . Now, expand the square inside the expectation; then the right-hand side is a function of , while the left-hand side isn't. The "best" (sharpest) inequality is the one when the right-hand side is lowest, so you have to choose which minimizes the right-hand side. This resumes to a standard function study (derivative, etc.) to find this minimum.