Mathematical notation of choosing randomly one element from a vector

Question

What is the mathematical notation for choosing randomly one element from a vector length $n$? For example our vector is $[3, 4, 5]$.

Answer 1

Usually we just say that $X$ is a random variable taking values $3$, $4$ and $5$. Of course you also have to specify the distribution, so you could say for example that $X$ is uniformly distributed on $\{3,4,5\}$. Various distributions also have names, and then you can use the notation $X \sim N(0,1)$, to for example indicate that $X$ is distributed like a standard normal random variable.