Probability Proof with E(x)

[claudiocamera]

Show that if x ≥ 0 and E(x) = η then P{ x≥ √η} ≤ √η.

How to prove this ?

 

[me2please]

It's just Markov's ineq

\[X \ge 0, \epsilon > 0, P(X \ge \epsilon) \le \frac{E(X)}{\epsilon}\]
\[P(X \ge \sqrt \eta) \le \frac{\eta}{\sqrt \eta}\]

proof of Markov's ineq can be found in almost all probability books.