Does anybody know how to do this sort of thing in Sage? Asked by me
today by a Stanford CS professor...
"It would be nice if it knew how to simplify the tail probability of a
binomial distribution. Mathematica can do:
FullSimplify[ Sum[Binomial[total, k] x^k (1 - x)^(total - k), {k, 0, n}]]
-> (1 - x)^total ((1/(1 - x))^
total - (1 - x)^(-1 - n) x^(1 + n)
Binomial[total, 1 + n] Hypergeometric2F1[1, 1 + n - total, 2 + n,
x/(-1 + x)])
With Sage it doesn't seem to have the hypergeometric functions (or
maybe it just doesn't know the simplification):
total, n, x, k = var('total', 'n', 'x', 'k')
simplify( sum( binomial(total,k) * x^k * (1-x)^(total - k), k, 0, n))
-> sum(x^k*(-x + 1)^(-k + total)*binomial(total, k), k, 0, n)
I was finding it was really slow to evaluate this with big values..."
--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org
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