A discrete random variable X is one with the following defining properties: - the set of values this variable can take is countable, i.e., either it is finite or it can be listed out in one-to-one correspondence with the positive integers, e.g., x_1, x_2, x_3,..., x_n,...; - the associated probability of each point x_k is such that 0 <= P(X = x_k) <= 1 for each k = 1, 2,..., n,...; and - _all, x P(X = x) = 1.

A discrete random variable \(X\) is one with the following defining properties:

the set of values this variable can take is countable, i.e., either it is finite or it can be listed out in one-to-one correspondence with the positive integers, e.g., \(x_1, x_2, x_3, ..., x_n, ...\);

the associated probability of each point \(x_k\) is such that \(0 \le \mathrm{P}(X = x_k) \le 1\) for each \(k = 1, 2, ..., n, ...\); and

\[\sum\limits_{\mathrm{all} \, x} \mathrm{P}(X = x) = 1.\]

Discrete Random Variables (DRV)

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Definition of probability distribution of a DRV

Definition of probability distribution of a DRV