A random variable X has the following probability distribution: X -2…

The correct answer is Option (3) → 1.89

$X:\;-2,-1,0,1,2$

$P(X):\;0.2,0.1,0.3,0.2,0.2$

$E(X)=(-2)(0.2)+(-1)(0.1)+0(0.3)+1(0.2)+2(0.2)$

$E(X)=-0.4-0.1+0+0.2+0.4$

$E(X)=0.1$

$E(X^2)=4(0.2)+1(0.1)+0(0.3)+1(0.2)+4(0.2)$

$E(X^2)=0.8+0.1+0+0.2+0.8$

$E(X^2)=1.9$

$\text{Var}(X)=E(X^2)-\{E(X)\}^2$

$\text{Var}(X)=1.9-(0.1)^2$

$\text{Var}(X)=1.9-0.01$

$\text{Var}(X)=1.89$