Proving if a function is a valid probability distribution

kioria

Hi,

Given the function:

[tex]P_{k} = \frac{20}{5^{k}}[/tex] for [tex]k \geq 2[/tex]

How would you prove that P is a probability distribution? I would think that you prove that P is bounded by 0 and 1 (i.e., [tex]0 \leq \Sigma P_{k} \geq 1[/tex])

And I guess the leading question is how you would prove that a function is not a probability distribution?

CRGreathouse

You also need that
[tex]\sum_{k=2}^\infty\frac{20}{5^k}=1[/tex]

HallsofIvy

You would prove that a function is NOT a valid probability distribution by showing that at least one of those conditions is not true. That is, that
1) P_k < 0 for some k or
2) P_k > 1 for some k or
3) [tex]\sum_{k=2}^\infty\frac{20}{5^k}\ne 1[/tex]

kioria

Cheers