Hello everyone,
I was working with the expressions Jim stated
and I've found the following. No doubt this is old
news to most readers of this list.
Maxima appears to expand summations into distinct
terms only if the limits are both definite. So, Jim,
perhaps that's why \sum_{i=1}^n was left in the
summation form. Maybe it's possible to tell Maxima
to use the linearity property of sum() to get it to
split something like \sum_{i=1}^n (a_i+b_i) into two
summations.
It might be easier to solve for the variance than
the standard deviation. What I mean is, state the
formulas in terms of a variable sigma2 instead of
sigma^2 and then solve for sigma2 instead of sigma.
With the upper limit equal to some definite value,
say 10, Maxima finds the usual formula for the sample
mean and a correct but messy formula for the sample
variance, equal to what you would get if you expanded
out E[X^2]-E[X] and did some rearranging. I don't
know how to encourage Maxima to find the "neat" form.
I think that Maxima has a lot of potential in
statistical problems even if explicit, symbolic
solutions are difficult to come by. Just being able
to compute derivatives symbolically is quite useful.
Derivatives come into play in parameter fitting and
other contexts. Integration is also important. One
general scheme, not yet realized, is to dump a model
into a machine which then generates all the code
necessary to do inference with the model. The idea
is to let the human think about the model, and the
machine attends to the details.
Hope this helps,
Robert Dodier
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