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?

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

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