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) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 094 0861 Date: 25-Jul-08 Time: 22:47:56 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
