Let $X$ be a random variable with pmf
$$ f(x) = \begin{cases} \binom nxp^x (1-p)^{n-x}, & \text{if } x=0,1,2,...,n \\ 0, & \text{elsewhere} \end{cases} $$
Find the pmf of $Y=\sqrt{X}$.
My attempt:
$$F(Y) = P(Y\le y) = P(\sqrt{X}\le y) = P(X\le y^2) =\binom n{y^2}p^{y^2} (1-p)^{n-y^2} $$
Am I on the right path?