Statistically independent events and distributions

An important statistical concept is that of independence. Two events or distributions are defined as independent if their joint probabilities equal the product of their individual probabilities. This may seem a mouthful, so a simple numerical example will help. If the chance that ‘x’ has a value of 3 is 0.2 and ‘y’ has a value of 2 is 0.3, then the chance ‘x’ is 3 and ‘y’ is 2 is 0.2 × 0.3 = 0.06. Often in simple probability theory, we can illustrate this by the toss of a die, so for example, the probability die A rolls a 2 is 1/6 and die B rolls a 3 is 1/6, so the probability that both events happen is 1/36.