Question: fsolve a posterior confidence using Jeffery's prior


I am using the Jeffery's prior for Binomial models, i.e. a beta prior distribution of beta(0.5, 0.5).

If we see n failure free trails, it is easy to know the posterior distriution is beta(0.5, 0.5+n).

Now I want to solve (plot..actually) the required n for specifced posterior confidence level and a bound.

I am using maple sources code as in the picture. But it takes very long time to plot n, given c=0.95, p=10^(-10)..10^(-7). Any idea to speed up the plots? Thanks!



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