# Variance of linear system

I have attached the problem of interest.
I think I am having trouble calculating the standard deviation for part a.

D=A-B-C
E(A)=10 E(B)=2 E(C)=2 sigma(A)=0.1 sigma(B)=0.05 sigma(C)=0.1
where sigma=standard deviation

so to find SD....:
V(D)=V(A-B-C)=sigma(A)2+sigma(B)2+sigma(C)2=(0.1^2)+(0.05^2)+(0.1^2)=0.0225
sigma(D)=(V(D))^0.5=0.0225^0.5=0.15

The book's answer is 0.1225. I do not see any glaring mistakes. Could someone please take a look?
The book may be wrong. I just want to make sure that it is not me that's wrong.

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## Answers and Replies

haruspex
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I have attached the problem of interest.
I think I am having trouble calculating the standard deviation for part a.

D=A-B-C
E(A)=10 E(B)=2 E(C)=2 sigma(A)=0.1 sigma(B)=0.05 sigma(C)=0.1
where sigma=standard deviation

so to find SD....:
V(D)=V(A-B-C)=sigma(A)2+sigma(B)2+sigma(C)2=(0.1^2)+(0.05^2)+(0.1^2)=0.0225
sigma(D)=(V(D))^0.5=0.0225^0.5=0.15

The book's answer is 0.1225. I do not see any glaring mistakes. Could someone please take a look?
The book may be wrong. I just want to make sure that it is not me that's wrong.
I agree with your answer.

• 1 person