Re: A problem with solving some nonlinear system

*To*: mathgroup at smc.vnet.net*Subject*: [mg87313] Re: A problem with solving some nonlinear system*From*: dh <dh at metrohm.ch>*Date*: Mon, 7 Apr 2008 05:18:21 -0400 (EDT)*References*: <fta9n1$eav$1@smc.vnet.net>

Hi, I assume that by f you mean the probability density functon of N[0,1]. This is specified by: PDF[ NormalDistribution[0,1] ] this returns a function, you may therefore say: fun1= PDF[ NormalDistribution[0,1] ] The integral of fun1 from -Infinity to x would then be the cumulative distribution function, denoted by: fun2= CDF[ NormalDistribution[0,1] ] the integral of fun1 from x to Infinity would be: 1-fun2[x] Therefore, your problem can be written by: eq={1-fun2[x1]==0.05,1-fun2[x2]==0.9}; t = {x1, x2} /. Solve[eq, {x1, x2}][[1]] this gives: t= {1.64485, -1.28155}, what makes sense. However,if n is a sample count, the final part does not make much sense. We must compute c and n from t: Solve[{(c-75)/10/Sqrt[n],(c-78)/10/Sqrt[n]}==t,{c,n}] this gives: {{n->0.0105093,c->76.6862}}. hope this helps, Daniel Walkman wrote: > Hi. This is the first posting in this board(in Englsigh?). So, if > there is any punctuation error or misunderstood, please let me know. > > The problem itself is in the book 428p. "Introduction to Mathematical > Statistics 6E" > > In solving this problem, I've got stuck with this practical problem. > > To find n and c such that > > Integrate[f,{z,(c-75)/10/sqrt(n),inf}] = .05 > Integrate[f,{z,(c-78)/10/sqrt(n),inf}] = .9 > > where f = N(0,1); N -> Normal Distribution of which mean = 0 and > variance = 1 > > How can I solve this problem in mathematica? or any math-computational > program? (e.g. R) >