Sum of indicator functions Suppose * $\\{x_i,i\geq1\\}$ \- _i.i.d._ values * **_u_** is some constant (f.e. $u = 0$) * **_n_** is predetermined constant as well (f.e. $n = 100$) How to calculate the following sum: $$\sum_{i=1}^n \mathbb{1}_{\\{x_i\geq u\\}}=\ldots~? $$

The desired sum is simply a binomial random variable with parameters $n$ and $$p = \Pr[X \ge u],$$ where $X$ is the common random variable corresponding to the sample $\\{x_i\\}_{i \ge 1}$.