Jacob Bernoulli, Binomial Distribution, Probability, Central Limit Theorem, Deep Dives.
setting. The ticket-filled urn is the sample space for what is clearly a binomial experiment, and the count X_bar_n of black tickets in the sample is Binomial(n, p). If the real fraction p of black tickets in the urn is known, then E(X_bar_n) is the expected value of a Binomial(n, p) random