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Probability: Infinite Convergent Series and Random Variables

by ZellDincht100
Tags: convergent, infinite, probability, random, series, variables
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ZellDincht100
#1
Feb22-10, 11:28 PM
P: 3
I have a random variable problem. I need to prove that my equation I came up with is a valid probability mass function.

In the problem, I came up with this for my probability mass function:

[tex]\Sigma[/tex] [tex]12/(k+4)(k+3)(k+2)[/tex]

Maple says that this does in fact converge to 1, so it's valid; however...I can't use "Maple said so" as an answer.

My attempt was to break it up using partial fraction decomposition:
([tex]6/(k+4)[/tex]) - ([tex]12/(k+3)[/tex]) + ([tex]6/(k+2)[/tex])

I was hoping that this would be telescoping, but it is not. Does anyone have an idea on how I can prove that this converges to 1?
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tiny-tim
#2
Feb23-10, 05:54 AM
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Hi ZellDincht100!
Quote Quote by ZellDincht100 View Post
My attempt was to break it up using partial fraction decomposition:
([tex]6/(k+4)[/tex]) - ([tex]12/(k+3)[/tex]) + ([tex]6/(k+2)[/tex])

I was hoping that this would be telescoping, but it is not.
Yes it is
[6/(k+4) - 6/(k+3)] - [6/(k+3) - 6/(k+2)]
ZellDincht100
#3
Feb23-10, 08:39 AM
P: 3
Quote Quote by tiny-tim View Post
Hi ZellDincht100!


Yes it is
[6/(k+4) - 6/(k+3)] - [6/(k+3) - 6/(k+2)]
Ahhhh I see! :D

Thanks! Dunno how I didn't see that before..


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