Random Variable

In many cases, the outcome of an experiment is already numeric, and we use the numbers "as they are", in other cases, some transformation is necessary. One example is the measurement of the temperature of a liquid. The fundamental basis is the speed of molecules. As a consequence of this physical property, we experience temperature. The function which assigns the average speed of molecules to a numerical value (the temperature) is called a continuous random variable.

In other cases, the outcome of an experiment is basically not a number but some "informal" property. In order to deal with such cases we have to find a "function" which assigns a number to each possible result.

Example: a person throws three dice. Suppose we are interested in cases, when two dice and when all three dice show the same number of eyes. We therefore define a function which assigns a value of three to the random variable in the case that all three dice show the same number of eyes, a value of two if only two dice satisfy the defined condition, and a zero value if this condition is not satisfied at all. The resulting variable is a discrete random variable.

Hint:    The terms random variable and random number are often mixed up, although they have nothing in common except the word "random".