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MathGroup Archive 2006

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Re: Binomial Distribution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71366] Re: [mg71356] Binomial Distribution
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Thu, 16 Nov 2006 00:52:44 -0500 (EST)
  • References: <200611151145.GAA01517@smc.vnet.net>

On 15 Nov 2006, at 20:45, Bruce Colletti wrote:

> Re Mathematica 5.2 under WinXP.
>
> Why doesn't the code below return a rational number?
>
> X = BinomialDistribution[10, 6/10];
> F[x_] := CDF[X, x];
> Rationalize@F@4
>
> Thankx.
>
> Bruce
>


I assume what you had in mind was:


<<Statistics`


X = BinomialDistribution[10, 6/10];


F[x_] := CDF[X, x]


Rationalize[N[F[4]]]

0.166239


Note the N. Rationalize will only work on approximate numbers. The  
reason why it does not work above is because there is no rational  
number "sufficiently close", where the meaning of "sufficiently  
close" is relative to the size of the denominator of the fraction  
(the larger the denominator the closer the number has to be to the  
one we are approximating to be considered "sufficiently close"). If  
you just want any rational approximation, without caring about the  
size of the denominator, you can use:


Rationalize[N[F[4]], 0]


75692233/455322801

Note that you got a pretty large denominator. If you would rather  
have a smaller one, you can get it but the approximation will be less  
accurate:


Rationalize[N[F[4]], 10^(-6)]


194/1167

Andrzej Kozlowski





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