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Probability Density Function, prove it

  • Thread starter randy27
  • Start date
9
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1. Homework Statement
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. Homework 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.
 

Answers and Replies

286
0
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)
 

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