Median from Probability distribution formula

Question

Can any one tell, how i can get formula for median of geometric distribution with this probability mass function formula $P_{r}=\frac{ (1-\alpha) \alpha^{CW}} { 1- \alpha^{CW} }. \alpha^{-r}$

Answer 1

Utilize the following:

Find $m$ such that

(1) $\displaystyle P(X \le m) \ge \frac{1}{2}$

(2) $\displaystyle P(X \ge m) \ge \frac{1}{2}$

The median will be any such $m$. This can be calculated using the PMF.

Edit

According to Truncated Distributions

The median of a truncated distribution will be

$\displaystyle F^{-1}\bigg( \frac{F(a) + F(b)}{2} \bigg )$