Prove Bernstein's inequality for any $t>0$. $P(X>y) \leq e^{-ty} E(e^{tX})$
This is for homework, but we did not go over Bernstein's inequality in class. We were going over Markov's and Chebyshev's inequalities. From what I have seen from looking it up on the internet there are several different ones, but I am not sure what applies to this particular problem.