# Thread: Statistics help? Probability mass function p.m.f expected value?

1. ## Statistics help? Probability mass function p.m.f expected value?

Let the p.m.f. (probability mass function) of X be de…noted by
f(x) = 1 / x(x + 1) ; for x = 1, 2, 3,...

1. Show that f is a p.m.f.
2. What is E [X] in this case?

Any help will be greatly appreciated!!!

2. you need to show that this sums to one, and it does

use partial sums to obtain

$\displaystyle {1\over x(x+1)} ={1\over x}-{1\over x+1}$

So $\displaystyle \sum_{x=1}^N {1\over x(x+1)} =\sum_{x=1}^N {1\over x} -{1\over x+1}= 1-{1\over N+1}\to 1$

as $\displaystyle N\to\infty$ since this is a telescoping series

The mean is infinite since that is a p-series (p=1)

So $\displaystyle E(X)=\sum_{x=1}^{\infty} {x\over x(x+1)} =\sum_{x=1}^{\infty} {1\over x+1}=\infty$

YOU can use the integral test and obtain $\displaystyle \log N\to\infty$

but that's where the p-series comes from.

3. I'm sorry, I didn't see that you wrote additional information. Thank you very much for the partial sums information!!!!!!

4. I type 2 or 3 lines at a time and then I edit my TeX.
There are plenty of typos and I need to edit it before I am done.