Problem: Expected value of a discrete random variable

Problem

\(X\) is a discrete random variable with range \(x_1=-1, x_2=1, x_3=4\) . Also, \(P\left( X=-1 \right)=1/4\) , \(P\left( X=1 \right)=1/2\) and \(P\left( X=4 \right)=1/4\) . Find \(E(X)\) .

Solution

\[E\left( X \right)=\left( -1 \right)⋅ \frac{1}{4}+1⋅ \frac{1}{2}+4⋅ \frac{1}{4}= \frac{5}{4}\]