Proving if a function is a valid probability distribution

[kioria]

Hi,

Given the function:

P_{k} = \frac{20}{5^{k}} for k \geq 2

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., 0 \leq \Sigma P_{k} \geq 1)

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

 

[CRGreathouse]

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

 

[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) \sum_{k=2}^\infty\frac{20}{5^k}\ne 1

 

[kioria]

Cheers