What is the mathematical notation for a random number in a certain range?

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 $10$?

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“Let $R$ be a random variable following the discrete uniform distribution over the set $\{5,6,7,8,9,10\}$.”

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 $p_1 + … + p_6 = 1$.