A map is linear if and only if and .

If is a non-negative random variable and is a positive number, then

The probability density function of the continuous uniform distribution is

• , if ,
• , if ,
• , if .

For the expected value we have

A random variable is discrete, if the set of output values is finite or countably infinite.

The function is called the probability density function of the random variable .

For any two events and one has .

If , then .

If are events, then occurs if occurs and does not occur.

If is a parametrized surface, then its area is