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