<p>A discrete random variable \(X\) is one with the following defining properties:</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">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., \(x_1, x_2, x_3, ..., x_n, ...\);</span></div></li><li><div class="list-item-content"><span class="list-item-text">the associated probability of each point \(x_k\) is such that&nbsp;\(0 \le \mathrm{P}(X = x_k) \le 1\) for each \(k = 1, 2, ..., n, ...\); and</span></div></li><li><div class="list-item-content"><span class="list-item-text">\[\sum_{\mathrm{all} \, x} \mathrm{P}(X = x) = 1.\]</span></div></li></ol>

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

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

Discrete Random Variables (DRV) - General

Discrete Random Variables (DRV)

International Baccalaureate Higher Level Mathematics

Definition of probability distribution of a DRV

Definition of probability distribution of a DRV