## Quick Reference

If *X* and *Y* are independent random variables each having the same uniform distribution then (*X*+*Y*) has a triangular distribution. In the case of a continuous random variable the graph of the probability density function is an isosceles triangle. In the case of a discrete random variable the graph of the probability function has a triangular shape. The diagram (*see diagram*) shows this for the case of throwing two ordinary dice. The most probable score is 7 (which results in a ‘Chance’ card when starting from ‘Go’ on a Monopoly board).

**Triangular distribution.** This is a graph of the distribution of the sum of the scores on two fair six-slide dice. The mode (corresponding to a probability of *6/36*) occurs when the sum is 7.

*Subjects:*
Probability and Statistics.

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