# Math Help - probability-lower bound on expected number

1. ## probability-lower bound on expected number

Hello everyone!

The problem is:

Suppose that the probability that a text contains 10 or more instances of the word "president" is 1/5. Provide a lower bound on the expected number of instances of this word

2. Originally Posted by tanichkap
Hello everyone!

The problem is:

Suppose that the probability that a text contains 10 or more instances of the word "president" is 1/5. Provide a lower bound on the expected number of instances of this word
The expected number of instances is:

$E(n)=\sum_{r=0}^{\infty} r p(r)$

This is obviously minimised subject to the constraint if $p(0)=0.8$, $p(10)=0.2$ and $p(r)=0$ for all other $r$.

So:

$E(n) \ge 2$

and the bound is tight.

RonL