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!!!
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!!!
you need to show that this sums to one, and it does
use partial sums to obtain
So
as since this is a telescoping series
The mean is infinite since that is a p-series (p=1)
So
YOU can use the integral test and obtain
but that's where the p-series comes from.