Expected value of a discrete random variable

Summary

Definition

• If \(X\) is a discrete random variable with range \({x_1,x_2,…,x_n}\) and probability mass function \(f(x)\) then the expected value of \(X\) is defined as

\[E\left( X \right)=\sum_{i=1}^{n}{ x_if(x_i) }\]

Example

• \(X\) is a random variable which can take values 1,2 or 3 and has a probability mass function given by
• \(f(1)=0.4\) ,
• \(f(2)=0.3\) and
• \(f(3)=0.3\) .
• The expected value of \(X\) is

\[E(X)=1×0.4+2×0.3+3×0.3=1.9\]