Binomial random variable multiplied by a positive constant

Question

Suppose we have $$X \sim Bin(n, p)$$ Let $Y \equiv \frac{X}{n}$ such that $n>0$ What's the distribution of $Y$? Using expectation and variance properties we got that: $EY = p$ $VY = \frac{p(1-p)}{n}$ Is also $Y$ binomial?