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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)

> 




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