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.
Cheers,
Jason
> Thanks,
> -Matthew J
> >
>
>
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