# Probability Density Function, prove it

1. Jan 15, 2007

### randy27

1. The problem statement, all variables and given/known data
This is my 1st post here, so I will do my best. The following question is part of a number of probability density functions that I have to prove. Once I have the hang of this I should be good for the rest, here is the question:

Prove that the following functions are probability density functions:

1/x^2 , x>0

2. Relevant equations

3. The attempt at a solution

As I understand to prove a probability density function it must satisfy

1. integral of f(x)dx=1
and
2. must not be negative f(x) for all x

I integrate the function of 1/x^2 which is -1/x but I find it tricky to explain myself on how f(x)dx=1

I would be greatfull on pointers on how to prove that the functions is a PDF in a clear manner.

2. Jan 15, 2007

### drpizza

You probably would have gotten a response quicker, but you posted this in the pre-calculus forum...

As I understand it, the integral needs to be = 1. (And, all values of f(x) > 0 which is your point 2.) However, I'm having trouble getting one when I integrate the function. Are you sure it's supposed to be x>0, and not x>1? Evaluating the improper integral from 1 to infinity =1 (unless I blundered somewhere; I did it really quick)