Updating rule for beta densities
Assume Beta(a,b) prior density of p
After observing s successes and f failures, updated density of p is beta(a+s,b+f):
pa–1(1–p)b–1x ps(1–p)f = pa+s–1(1–p)b+f–1
Special case of Beta(a,b) is the uniform: a = b = 1 (considered previously)