Pierre Simon Laplace, Inverse Probability, Central Limit Theorem, Probability, Deep Dives.
observed ratio X_bar_n/n. For exampl, recollect that in case of the Paris census data, X_bar_n/n = 251527/493472 = 0.50971. Thus, we’d want to know the following probability: P(p | n=493472, X_bar_n=251527) Notice how this probability is the exact inverse of the ‘forward’ binomial probability: