Double Integrals and Expected Values in Probability Theory

 Expected Values Values

In probability theory, we define the expected values E(x) and E(y) as the most likely outcomes of the events. They are given by the following formulas:

where S is the sample space of the random variables X and Y.

Example..

We resume the example from the last post:

What is the expected time for the events "waiting for a table" and "completing the meal"

Solution

Using the first quadrant of coordinate plane as as the sample space, let's call E(X) the expected time for "waiting for a table"  and E(Y) the expected time for "waiting for a table". Let's calculate E(X)and E(Y):