The loads on an electrical network with 10 regions are modelled by considering a base load with mean 20mW and standard deviation 3mW. Variation due to regional load is modelled by considering that each region contributes an additional amount to the total load, which is normally distributed with mean 5mW and standard deviation of 1.5mW. The regional loads are independent of the base load, but have a correlation of 0.1 with loads of adjacent regions. the regions are coded 1-10 in suach a way that the correlation is between regions with adjacent codes, with being adjacent to 1 as well as 9. Obtain the standard distribution of the total load.
My working is : Cor(R1,R2)=0.1*0.0015 Var (B+R)= Var (B) + 10 Var (R) + 2*10*Cor (R1+R2) = 9+22.5+20*0.1*0.0015 But the answer is 6mW, where did I go wrong?
I would have thought that the variance of the sum was $3^2+10\times 1.5^2 +20\times 0.1 \times 1.5^2$. You would then need to take the square root for a standard deviation.
The problem seems to be with your $0.0015$.
My guess is that the units of power should be megawatts (MW) rather than milliwatts (mW), and the square of this for variance and covariance.