Independent solution

How to solve this Covariance question

Setup

Setup

Use the variance of the original sum to recover the covariance between the two components.

17000=5000+10000+2Cov⁡(X,Y)17000=5000+10000+2\operatorname{Cov}(X,Y)

Model

Model

The revised total adds a constant and multiplies the second component by 1.1. The constant has no effect on variance, while the component variance and covariance terms must be scaled by their coefficients.

Cov⁡(X,Y)=1000\operatorname{Cov}(X,Y)=1000
T=X+100+1.1YT=X+100+1.1Y

Compute

Compute

Substituting the recovered covariance into the variance expansion gives 19,300.

Var⁡(T)=5000+1.12(10000)+2(1.1)(1000)=19300\operatorname{Var}(T)=5000+1.1^2(10000)+2(1.1)(1000)=19300

Answer

Answer

The revised total has variance 19,300, selecting choice C.

19,300(C)\boxed{19{,}300\quad\text{(C)}}