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.