I have $n$ random variables $X_i$, each following the same probability distribution but with different parameters. These variables can take only positive values.
Now, let's say I take one realization of each variable $[x_1, x_2, ..., x_n]$. I want to express a new variable $Y$ being the proportion of values in this vector which are inferior to 3 : $$ Y = \dfrac{\# x_i \text{ such that } x_i \leq 3}{n}, $$
or
$$ Y = \dfrac{\sum \limits_{i=1}^n \mathbb{1}_{X_i \leq 3}}{n}. $$
So how can I express $Y$ thanks to the distributions of each random variable $X_i$? I.e., what is the distribution of $Y$?
Thanks a lot!