Saturday, November 1, 2014

linear combo of (Normal or otherwise) rvar - var + stdev

Q: given the variance of random variable A, what about the derived random variable 7*A?

Develop quick intuition -- If A is measured in meters, stdev has the same dimension as A, but variance has the square-meter dimension.

⇒ therefore, V( 7*A ) = 49 V(A) and stdev( 7*A ) = 7 stdev(A)

Special case - Gaussian:  A ~ N(0, v), then 7*A ~ N(0, 49v)

More generally, given constants C1 ,  Cetc, A general linear combo of (normal or non-normal) random variables has variance

V(C1A + C2B+...) = C1C1V(A) + C2C2V(B)+.. +2(unique cross terms), where

unique cross terms are the (n2-n)/2 terms like C1C2*Cov(A,B)

Rule of thumb -- nterms in total

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