A random variable can have an even more complicated structure. Specific examples are given in the computational exercises below. However, the key point is simply that a random variable is a function from the sample space S to another set T . Inverse Images Suppose that f is a function from a set S into a set T . In words, a statement about the random variable defines an event .
Inverse images preserve all set operations.
In the following exercises, f is a function from S into T . Suppose that X is a random variable taking values in T , for a random experiment with sample space S . Basic and Derived Variables Suppose again that we have a random experiment with sample space S . The outcome of the experiment itself can be thought of as a random variable. A for A S .