- #1

TelusPig

- 15

- 0

## Homework Statement

If [itex]g(x)\ge 0[/itex], then for any constant ##c>0, r>0##:

[itex]P(g(X)\ge c)\le \frac{E((g(X))^r)}{c^r}[/itex]

## Homework Equations

I know that [itex]E(g(X))=\int_0^\infty g(x)f(x)dx[/itex] if [itex]g(x)\ge 0[/itex] where ##f(x)## is the pdf of ##X##.

## The Attempt at a Solution

I tried following a similar proof to what I found here (on page 2: http://www.stat.cmu.edu/~larry/=stat705/Lecture2.pdf).

I'm really stuck on this. I've tried to look on the Internet for a proof, but the inequalities I find involve X, not g(X) and there isn't any exponent ##r##. I tried doing something similar by replacing X with g(X) but it doesn't quite work out. I still need an exponent ##r## and I don't know how the last step would get me to write something like [itex]c^r P(g(x)\ge c)[/itex]