Definition:Geometric Distribution

Let $$X$$ be a discrete random variable on a probability space $$\left({\Omega, \Sigma, \Pr}\right)$$.

Then $$X$$ has the geometric distribution with parameter $$p$$ (where $$0 < p < 1$$) if:


 * $$\operatorname{Im} \left({X}\right) = \left\{{1, 2, \ldots}\right\} = \N^*$$


 * $$\Pr \left({X = k}\right) = p \left({1 - p}\right)^k$$

Note that the Geometric Distribution Gives Rise to Probability Mass Function satisfying $$\Pr \left({\Omega}\right) = 1$$.