Jacob Bernoulli, Binomial Distribution, Probability, Central Limit Theorem, Deep Dives.
variable which is np. With E(X_bar_n) known, the probability distribution P(X_bar_n|p,n) is fully specified. Then it’s theoretically possible to crank out probabilities such as P(np — δ ≤ X_bar_n ≤ np + δ) as follows: P(np-δ ≤ X_bar_n ≤ np+δ) where X_bar_n ~ Binomial(n,p) (Image by Author) I