Statistically independent events and distributions
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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.
[1] R. Brereton. The chi squared and multinormal distributions , 2015 .