# Probability Proof with E(x)

Status
Not open for further replies.

#### claudiocamera

##### Full Member level 4
Show that if x ≥ 0 and E(x) = η then P{ x≥ √η} ≤ √η.

How to prove this ?

##### Full Member level 3
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.

Last edited by a moderator:

### claudiocamera

points: 2
Status
Not open for further replies.