Suppose that, using MATLAB or ... , I created a vector of exponentially distributed random variables with length of $N$, i.e., $X=a_1,a_2 , ... a_N $, and I computed the cumulative distribution function for a given threshold $x$:
$$F_X(x) = P_r(X<x) $$
Now, how can I compute the associated error for this Monte-Carlo simulations?
Matlab Code
N = 100;
lambda = 0.2;
X = abs( sqrt(0.5*lambda) * (randn(1,N) + 1i*randn(1,N)) ).^2;
Temp = X <= x;
F_X_x = (1/N)*sum(Temp)