TITLE: What is the mathematical notation for a random number in a certain range?
QUESTION [6 upvotes]: In school, I was taught to denote a random variable like so:
$$R=\{_{0}^{1}$$
This only goes for a random choice between two integers, like a coin flip. How do I write a variable that is equal to a random integer in a certain range, such as, $5$ to $10$?

REPLY [2 votes]: It looks like you were taught about the Bernoulli distribution, in which a random variable (call it $R$) can take a value of either $0$ or $1$. Note that we have a probability function which tells us the probability of $R$ being either $0$ or $1$. Explicitly, this looks like $P(R = 1) = p$, and $P(R = 0) = 1-p$.
Now, if we want to let our random variable $R$ have the possibility of taking on multiple values (say $R \in \{5,...,10\}$), then we can assign values for $p_1 = P(R=5), p_2 = P(R=6), ..., p_6=P(R=10)$ where $p_1 + ... + p_6 = 1$.