Independent solution

How to solve this Variance question

Setup

Setup

Write the second-period cost as an affine transformation of the first-period random cost.

Y=1.03X+2.5,Var⁡(X)=50Y=1.03X+2.5,\qquad \operatorname{Var}(X)=50

Model

Model

Variance is multiplied by the square of the random coefficient and is unchanged by a constant shift.

Var⁡(aX+b)=a2Var⁡(X)\operatorname{Var}(aX+b)=a^2\operatorname{Var}(X)

Compute

Compute

Apply the transformation rule.

Var⁡(Y)=(1.03)2(50)=1.0609(50)=53.045\operatorname{Var}(Y)=(1.03)^2(50)=1.0609(50)=53.045

Answer

Answer

The listed value is 53.

53(B)\boxed{53\quad\text{(B)}}