- #1
ZellDincht100
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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?
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?