# Probability for individual elements

I have Probability equation given by $$p(r)=\frac{ (1-\alpha) \alpha^{CW}} { 1- \alpha^{CW} }. \alpha^{-r}$$ . Here r is number of objects from 1 to $$CW$$.

How can i write probability of picking any one of the elements from $$r= 1,......,CW$$ , here $$CW=10$$.

If it were uniform distribution we could write it as $$p=1/CW=1/10$$, but here every element has different probability due geometric truncated distribution equation shown above.

• Could you clarify a bit what you are asking? $p(r)$ is a discrete probability distribution, since $\sum_{r=1}^{CW}p(r) = 1$. So, you can think of a random variable $X$ which can assume the values $X=1,\ldots , CW$ with the corresponding probabilities $P(X=r)=p(r)$. Feb 9, 2020 at 5:41
• The question is unclear. The natural interpretation of the first paragraph is that $p(r)$ is already the desired probability of picking one of the elements from $1$ to $CW$; thus it's unclear what you're asking for in the second paragraph. Feb 9, 2020 at 9:49