Random variable

Henceforth the symbol X(w) will be used for the random variable X#58;S#92;rightarrow#92;mathbb#123;R#125;.

The particular example considered here is the Hilbert space of random variables.

A two-dimensional random variable is a mapping of the points in the sample space to ordered pairs {x, y}. Usually, when dealing with a pair of random variables, the sample space naturally partitions itself so that it can be viewed as a combination of two simpler sample spaces.