Calculation of Covariance

Question

To cut to the chase, $T_1$ is independent of $T_2$ and $T_3$. However, $T_2$ and $T_3$ has correlation of $0.5$.

$V[T_1] = 36$

$V[T_2] = 100$

$V[T_3] = 64$

$V[T_{total}] = V[T_1] + V[T_2] + V[T_3] + 2Cov[T2,T3]$ which by my calculation gives $36 + 100 + 64 + 80 = 280$. However, the answer given is $36 + 100 + 64 + 1 = 201 $

Note: To calculate $Cov[T_2,T_3]$, I used the formula $Corr[T_2,T_3]=\frac{Cov[T_2,T_3]}{\sqrt{V[T_2]V[T_3]}}$

Can someone point out my error? Thanks!

Answer 1

Yes.   Either the book's answer or question is contains an error.   The answer given is for if the question had said the covariance was $0.5~$.

Your answer is for if the correlation was $0.5~$.   It is the correct answer for the question as written.