What does it mean to take a sample from $F$

Question

In a stats textbook discussing monte carlo integration, it says "A sample $X_1, X_2, ... , X_N$ ~ $F$ can be used to estimate all quantities of interest from $F$", but I'm not sure what this means. I've only ever seen something like $X$ ~ $Exp(\lambda)$, where the random variable $X$ follows the exponential distribution, but isn't $F$ just the CDF of a certain distribution?

Answer 1

The CDF $F$ of a distribution characterizes the distribution. It is equivalent to specify the CDF or to specify the distribution. So $X\sim F$ is just a shorthand for "$X$ follows the distribution whose CDF is $F$".