I am looking at a reference for sampling from a distribution, and the first step of the so-called algorithm states:http://www.columbia.edu/~ks20/4703-Sigman/4703-07-Notes-ARM.pdf
- Generate a random variable $Y$ from distribution $G$.
How does this sentence make sense to people in statistics?
To me, a random variable is a function or mapping from the set of outcomes $\xi$ to a real number $y$. That is, $Y: \xi \mapsto y$.
What then, does it mean to generate a "random variable"?
It would mean to synthesize a function. I fail to see how this is even programmability feasible. For instance, what does it mean to generate "sine" function in Python? The most I could do is to provide you some samples from that sine function, but I could never provide the function itself, which is an abstract thing.
In addition, to generate something from distribution to me means to "produce a number".
So the wording is very confusing to me. Because a function is not a number.
Can someone clarify this idea for me?