Jacob Bernoulli, Binomial Distribution, Probability, Central Limit Theorem, Deep Dives.
X_bar_n is the sum, not the mean, of n i.i.d random variables. Thus: X_bar_n/n is the proportion of black tickets that you have observed, and |X_bar_n/n — p| is the unknown error in your estimation of the real, unknown ratio p. What Bernoulli theorized was that as the sample size n becomes very