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Probability: Infinite Convergent Series and Random Variables 
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#1
Feb2210, 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? 


#2
Feb2310, 05:54 AM

Sci Advisor
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Thanks
P: 26,160

Hi ZellDincht100!
[6/(k+4)  6/(k+3)]  [6/(k+3)  6/(k+2)] 


#3
Feb2310, 08:39 AM

P: 3

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


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