Let X~geometric (1/3), and let Y=|X-5|. Find the range n and PMF of Y. Let X~geometric (1/3), and let Y=|X-5|. Find the range n and PMF of Y.
Here is my trial 
If $x=0$, $P(Y=|0-5|)=P(Y=5)=\left(\frac{2}{3}\right)^5 \frac{1}{3}$
If $x=1$, $P(Y=|1-5|)=P(Y=4)=\left(\frac{2}{3}\right)^4 \frac{1}{3}$
If $x=2$, $P(Y=|2-5|)=P(Y=3)=\left(\frac{2}{3}\right)^3 \frac{1}{3}$
If $x=3$, $P(Y=|3-5|)=P(Y=2)=\left(\frac{2}{3}\right)^2 \frac{1}{3}$
If $x=4$, $P(Y=|4-5|)=P(Y=1)=\left(\frac{2}{3}\right)^1 \frac{1}{3}$
If $x=5$, $P(Y=|5-5|)=P(Y=0)= \frac{1}{3}$
Range of $Y={0,1,2,3,4,5}$
and PMF is I $P(Y=y)=\left(\frac{2}{3}\right)^y \frac{1}{3}$ for $y=0,1,2,3,4,5$
Am I correct. If not please correct me. 

Range of $Y$ is $(0,\infty)$.
$$P(Y=k) \;=\; (2/3)^{k-1} * (1/3).$$
