Algebraic problem solved by simulation

*To*: mathgroup at smc.vnet.net*Subject*: [mg53604] Algebraic problem solved by simulation*From*: guillerm at aida.usal.es (Guillermo Sanchez)*Date*: Thu, 20 Jan 2005 03:47:44 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

(* Dear group; Given the equation L1 < a1 X1, ..., an Xn < L2 where {a1, ..an} are known and {X1, ...Xn} follows a Uniform random distribution I wish to find the average and the estandar deviation of X, being X = X1 + ... + Xn. For instance, for solving 0.95 < 0.017 X1 + 0.013 X2 + 0.012 X3 < 1.05 I apply this method*) a = {0.017, 0.013, 0.012}; rr := {Random[Real, {0, 1/0.017}], Random[Real, {0, 1/0.013}], Random[Real, {0, 1/0.012}]}; eq1 := (X = rr; If[0.95 < a . X < 1.05, Plus @@ X] ) ; L = Array[eq1 &, 1000] ; sol1 = Cases[L, x_?NumericQ]; {Mean[sol1], StandardDeviation[sol1]} (*Can any body find a better method?, In the real problems the size of {X1, ..., Xn} is too big (1000) Guillermo*)

**Follow-Ups**:**Re: Algebraic problem solved by simulation***From:*DrBob <drbob@bigfoot.com>