SL 4.7—Discrete random variables

Discrete Random Variable: A variable whose value is determined by the outcome of a random experiment, and which can only take a countable set of specific, separate values , typically whole numbers.

Think of a discrete random variable as a quantity that jumps between distinct values rather than flowing continuously. You can list all its possible outcomes.

Examples of discrete random variables:

• The number shown when rolling a fair six-sided die: $X\in \{1,2,3,4,5,6\}$
• The number of heads in 5 coin flips: $X\in \{0,1,2,3,4,5\}$
• The number of goals scored in a football match: $X\in \{0,1,2,3,...\}$

Contrast with continuous random variables (not covered here): those can take any value in a range, like height or temperature.