# Applications of Mathematical Expectation

• Enders A. Robinson

## Abstract

The idea of an average is especially pertinent to the subject of random variables and readily lends itself to broad development. By the ordinary rule, the arithmetic average of a set of N numbers x 1, x 2, x N is obtained by computing their sum and then dividing by N; that is, $$\bar x$$ = (x 1 + x 2 + ··· + x N )/N. Now since it is not necessary that these numbers all be different, let us suppose, in general, that there are n distinct values, x 1, x 2, •••, x n respectively occurring N 1, N 2, •••, N n times, where N 1 + N 2 + ••• + N n = N. Then the sum of the N numbers could be found by adding up the products N 1 x 1 N 2 x 2, •••, N n x n and the arithmetic average would be obtained by dividing the result by N.

## Keywords

Probability Density Function Mathematical Expectation Expected Profit Profit Function Unimodal Distribution
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