We have [tex]y\in\{0,1,2\}[/tex], and for each possible outcome we can determine the corresponding probability using the fact that [tex]X[/tex] is uniformly distributed among [tex]x\in\{0,1,\ldots,9\}[/tex].
[tex]y=\begin{cases}0&\text{for }x\in\{0,3,6,9\}\\1&\text{for }x\in\{1,4,7\}\\2&\text{for }x\in\{2,5,8\}\end{cases}[/tex]
[tex]\implies\mathbb P(Y=y)=\begin{cases}\dfrac4{10}=\dfrac25&\text{for }y=0\\\\\dfrac3{10}&\text{for }y=1\\\\\dfrac3{10}&\text{for }y=2\end{cases}[/tex]
