# How i can get formula for median of geometric distribution with this probability mass function formula P_r=((1-alpha)alpha^{CW})/(1-alpha^{CW}) cdot a^{-r}

Chaim Ferguson 2022-10-17 Answered
Median from Probability distribution formula
How i can get formula for median of geometric distribution with this probability mass function formula ${P}_{r}=\frac{\left(1-\alpha \right){\alpha }^{CW}}{1-{\alpha }^{CW}}.{\alpha }^{-r}$
You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Step 1
Utilize the following:
Find m such that
(1) $P\left(X\le m\right)\ge \frac{1}{2}$
(2) $P\left(X\ge m\right)\ge \frac{1}{2}$
The median will be any such m. This can be calculated using the PMF.
Step 2
According to Truncated Distributions
The median of a truncated distribution will be ${F}^{-1}\left(\frac{F\left(a\right)+F\left(b\right)}{2}\right)$