"Basically what we are doing is using a Beta prior (with parameters $a=1, b=1$, which is a uniform distribution), and using a Binomial likelihood with observations $u, N = u+d$. This means our posterior is a Beta distribution with parameters $a' = 1 + u, b' = 1 + (N - u) = 1+d$. We then need to find the value, $x$, such that 0.05 probability is less than $x$. This is usually done by inverting the CDF ([Cumulative Distribution Function](http://en.wikipedia.org/wiki/Cumulative_Distribution_Function)), but the CDF of the beta, for integer parameters, is known but is a large sum [3]. \n",
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