# discrete distribution - find the constant

• Jun 18th 2008, 08:18 AM
math beginner
discrete distribution - find the constant
This is a question from Degroot and Schervish's Probability and Statistics Textbook: p 103 qn 9

Suppose that a random variable X has a discrete distribution with the following probability function:

f(x) = ( c/(x squared) for x=1,2,...
( 0 otherwise

Find the value of the constant c.

I tried working it out and my answer is c = 1.
But the back of the textbook states the answer as 6 / pi squared.
Please could someone help me understand why?
• Jun 18th 2008, 08:32 AM
Plato
Well, this is a well known sum: $\sum\limits_{x = 1}^\infty {\frac{1}{{x^2 }}} = \frac{{\pi ^2 }}{6}$.
It's a routine result using the Fourier Series for $f(x) = x^2$.