Range & PMF of Y for X ∼ Geometric(1/3)

[Jonobro]

Homework Statement

Let X∼Geometric(1/3), and let Y=|X−5|. Find the range and PMF of Y.

Homework 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

 

[Ray Vickson]

Homework Statement

Let X∼Geometric(1/3), and let Y=|X−5|. Find the range and PMF of Y.

Homework 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

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