Independent (probability)

In probability theory, two events E and F are called independent if

Pr(E and F) = Pr(E) · Pr(F).

Intuitively, this means that knowing whether E occurred or not does not influence the probability of F, and vice versa. For instance, if you roll a green and a red die, the event E that the green die shows a three and the event F that the red die shows an even number are independent.

Two random variables X and Y are called independent if for all real numbers a, b, c and d, the events { a ≤ X ≤ b } and { c ≤ Y ≤ d } are independent. Intuitively, this means that knowing something about the value of X does not give any information about the value of Y. A typical example of two independent variables is given by repeating an experiment: roll a die twice, let X be the number you get the first time, and Y the number you get the second time. These two variables are independent.