# Exercise C.4.1

Verify axiom 2 of the probability axioms for the geometric distribution.

$$\sum_{k=1}^{\infty} \Pr\{X = k\} = \sum_{k=1}^{\infty} q^{k-1}p = p \sum_{k=0}^{\infty} q^k = p \frac{1}{1-q} = \frac{p}{p} = 1$$