On Tue, Dec 9, 2008 at 2:04 PM, Jason Bandlow <[EMAIL PROTECTED]> wrote:
>
> Hi Matthew,
>
> Matthew J wrote:
>> Sage is great software that I rave about in pretty much all of my
>> classes except for probability theory. I'd like to get some info on a
>> few topics to clear some things up so that I can use these for classes
>> and to post to an examples worksheet. Thanks in advance to anyone that
>> replies.
>>
>> I am wondering how to do a few things.
>> Is there a better (built-in) way to do simple combinations/
>> permutations than writing a function like
>>
>> def choose(n,k): return factorial(n)/(factorial(k)*factorial((n-k)))
>>
> Entering: binomial(5,2)
> will return: 10
>
> Is this what you want? (This is much more efficient than the 'choose'
> function you have above.)
>> or equivalent for permutations?
>>
>
> I'm not sure exactly what you mean here. factorial(n) counts the number
> of permutations of 'n' elements very efficiently. Perhaps you mean
>
> sage: permutations([1,2,2])
> [[1, 2, 2], [2, 1, 2], [2, 2, 1]]
>
> Type permutations? for more information on this command. You may also
> be interested in the command 'combinations'.
>
>> -----
>>
>> Is there a way to get the Standard Normal CDF other than writing the
>> function explicitly like below?
>>
>> def normalCDF(z):
>> t = var('t')
>> return N(integrate((1/sqrt(2*pi))*e^((-t^2)/2), t, -infinity, z))
>> -----
>>
>> Also, are there any distributions built into sage? I don't quite know
>> what working with a distribution symbolically would be like, but as an
>> example, perhaps being able to do something like
>> X ~ BIN(n, p) and then get the expected value, variance, or PDF of X?
>> Assume that n and p are given.
>>
>
> *Lots* of statistics is built into sage with the 'R' package. I don't
> know it well, but you can try typing R? inside sage and see what you can
> work out from there.
>
Sage also includes the scipy.stats package, which has 100 or
so distributions:
sage: import scipy.stats
sage: help(scipy.stats)
William
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