Rolling a die (many dice)


Sample Space

, 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.

Random Variable

A discrete random variable can also be used to describe the process of rolling dice and the possible outcomes.

Sum of two dice

Example if the random variable X is the sum S of the numbers on the two dice.

Given that the sample space for one dice (representing the numbers on one die) is <MATH> n_i = {1, 2, 3, 4, 5, 6} </MATH> the random variable function maps the pair to the sum: <MATH> X((n_1, n_2)) = n_1 + n_2 </MATH> and its probability mass function (given the dice are fair) is

<MATH> 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>

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