An arbitrary number of other stochastic variables may be derived from \( X \). For example, any \( Y \) given by a mapping of \( X \), is also a stochastic variable. The mapping may also be time-dependent, that is, the mapping depends on an additional variable \( t \)
$$ Y_X (t) = f(X, t). $$The quantity \( Y_X (t) \) is called a random function, or, since \( t \) often is time, a stochastic process. A stochastic process is a function of two variables, one is the time, the other is a stochastic variable \( X \). Let \( x \) be one of the possible values of \( X \) then
$$ y(t) = f (x, t), $$is a function of \( t \), called a sample function or realization of the process. In physics one considers the stochastic process to be an ensemble of such sample functions.