A) Prove Bernstein's inequality: If X is a random variable for which Mx(t) exists for some t>0, the P(X>=x) <= Mx(t)e^(-tx). Assuming X is continuous.
B) If X~N(0,1), then Mx(t)=e^((t^2)/2) for all t.
Thus, by A), P(X>=x)<=e^((t^2)/2 - tx).
For x=2, find the value of t for which this inequality is sharpest.