Re: [R] Numerical question

From: Ted Harding <Ted.Harding_at_manchester.ac.uk>
Date: Fri, 25 Jul 2008 22:47:59 +0100 (BST)


On 25-Jul-08 21:06:38, Zhang Yanwei - Princeton-MRAm wrote:
> Hi all,
> I have n independent variables A_1, A_2, A_3,......,A_n, and each
> with known variances var(A_1), var(A_2),..., but unknown mean. How can
> I get the approximation of the variance of the product of the variables
> using numerical computation, i.e. var(A_1*A_2*A_3*.....*A_n)? Thanks.

Without knowing the means, you cannot. Let M1, M2, ... , Mn be the means of A1, A2, ... , An, and let V1, V23, ..., Vn be their variances.

Then (to a first approximation)

Var(A1*A2*...*An) =

  (M1^2)*(M2^2)*...*(Mn^2) * (V1/(M1^2) + V2/(M2^2) + ... + Vn/(Mn^2))

so the variance depends on the means Mi as well as on the variances Vi.

Ted.



E-Mail: (Ted Harding) <Ted.Harding_at_manchester.ac.uk> Fax-to-email: +44 (0)870 094 0861
Date: 25-Jul-08                                       Time: 22:47:56
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