Editing Random variable (section)

====Dice roll====

[[File:Dice Distribution (bar).svg| right | thumb | If the sample space is the set of possible numbers rolled on two dice, and the random variable of interest is the sum ''S'' of the numbers on the two dice, then ''S'' is a discrete random variable whose distribution is described by the [[probability mass function]] plotted as the height of picture columns here.]]

A random variable can also be used to describe the process of rolling dice and the possible outcomes. The most obvious representation for the two-dice case is to take the set of pairs of numbers ''n''<sub>1</sub> and ''n''<sub>2</sub> from {1, 2, 3, 4, 5, 6} (representing the numbers on the two dice) as the sample space. The total number rolled (the sum of the numbers in each pair) is then a random variable ''X'' given by the function that maps the pair to the sum:
<math display="block">X((n_1, n_2)) = n_1 + n_2</math>
and (if the dice are [[fair die|fair]]) has a probability mass function ''f''<sub>''X''</sub> given by:
<math display="block">f_X(S) =  \frac{\min(S-1, 13-S)}{36}, \text{ for } S \in \{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}</math>