Chapter 3 - Section 3-4 - Mean and Variance of a Discrete Random Variable - Exercises - Page 77: 3-59

μ=-0.4, σ²=1.64

Given, $P(x=-2)=0.2,P(x=-1)=0.4,P(x=0)=0.1,P(X=1)=0.2,P(x=2)=0.1$, then, $μ=E(x)=∑xP(x)=(-2)×0.2+(-1)×0.4+0×0.1+1×0.2+2×0.1=-0.4$, $σ²=V(x)=∑x²P(x)-μ²=(-2)²×0.2+(-1)²×0.4+0²×0.1+1²×0.2+2²×0.1-(-0.4)²=1.64$