How to find probability distribution of $Y=3$X, if Poisson distribution of $X$ has parameter $\lambda$?

Question

Random variable $X$ has Poisson distribution parameter $\lambda$. Find the probability distribution of random variable $Y=3X$.

Answer 1

If $3\mid k$ then:

$$P(Y=k) = P(3X =k) = P(X={k\over 3}) = e^{-\lambda}{\lambda^{k\over 3}\over {k\over 3}!}$$

else $P(Y=k)=0$.