# If a random variable ranges in a integer, is the random variable discrete or continuous? [closed]

The book “Introduction to Probability, $$2$$nd Edition” says:

A random variable is called discrete if its range is either a finite or countable infinite.

Assume a random variable $$X$$, $$P(X=k) = p^k(1-p)^{n-k} \text{ where } k \in \Bbb Z.$$

Is the random variable $$X$$ discrete or continuous?

• Is the set $\Bbb{Z}$ finite or countably infinite? – frabala Mar 3 '19 at 9:24