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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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