# Geometric PMF

1. Sep 29, 2015

### Jonobro

1. The problem statement, all variables and given/known data
Let X∼Geometric(1/3), and let Y=|X−5|. Find the range and PMF of Y.

2. Relevant equations
Px(k) = p(1-p)^(k-1) for x=1,2,3...

3. My attempt at a solution
I set up the PMF for Px

Px(k) = 1/3(2/3)^(k-1) for k = 1,2,3,...
However I don't know how to convert this to Y

2. Sep 29, 2015

### Ray Vickson

Really? For what values of $X$ do you get $Y = 0$? Which value (or values) of $X$ give you $Y = 1$? Etc., etc.