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Just a note

Each of these two curves is the result of testing 1000 different null hypotheses, none of which assumed that P=p=0 - instead these tests used P = 0.005, 0.01, 0.015, ... 0.995.

In other words our observed result of p=f=0 (in a sample of n=5) was subject to a 2-tailed exact binomial test, whose null distribution was binomial and P was the probability each of our n=5 (randomly and independently selected) values would equal 1. Remember, testing p=0 assuming that P=p=0 has a 100% predictable outcome: A conventional exact binomial test gives a P-value of 1, and a mid-P exact binomial test gives a P-value of 0.5.

Below are the instructions that produced this plot.