An extremely useful
concept in problems involving random variables or distributions is that of
expectation. Random variables can be characterized and dealt with effectively
for practical purposes by consideration of quantities called their expectation.
The concept of mathematical expectation arose in connection with games of
chance. For example, a gambler might be interested in his average winnings at a
game, a businessman in his average profits on a product, and so on. The average
value of a random phenomenon is also termed as its Mathematical expectation or
expected value. In the following sections, we will define and study the concept
of mathematical expectation for both discrete and continuous random variables,
which will be used in the following subsection.