Question

ST. Calculate the variance of a random variable ξ, such that P(ξ=0)=0.2,P(ξ=1)=0.3,P(ξ=2)=0.5.

Answer 1

$$E(\xi)=0.2(0)+0.3(1)+0.5(2)=1.3$$

$$E(\xi^2)=0.2(0)^2+0.3(1)^2+0.5(2)^2=2.3$$

$$Var(\xi)=E(\xi^2)-(E(\xi))^2$$

$$=2.3-(1.3)^2=0.61$$

$$Var(\xi)=0.61$$