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

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- Jul 15th 2008, 08:33 AMtanichkapprobability-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 - Jul 15th 2008, 09:20 AMCaptainBlack
The expected number of instances is:

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

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

So:

$\displaystyle E(n) \ge 2$

and the bound is tight.

RonL