The characteristic function (also called indicator function ) of a subset of that referred to in the mathematical function by which is precisely when element of, and otherwise
The notations and are also common.
The assignment gives a bijection between the power set and the set of all functions of the amount
In the formation of the partial amount characteristic function is limited to the definition; in the sense of partial functions they can be thus described as follows:
Expected value, variance and covariance
For a given probability space and the indicator function is defined by if and otherwise is a random variable. For them, the following applies:
We see that the variance of is maximum in the case and two indicator variables are uncorrelated if and only if the associated events are stochastically independent.