Convergence, Probability, Cumulative Distribution, Statistics, Editors Pick.
= 1 and P(X_k=1) = 0. Thus, the first coin in the sequence is biased to always come up as Tails. When k = ∞, (1 — 1/k) = 1. This time, P(X_k=0) and P(X_k=1) are both exactly 1/2, Thus, the infinite-th coin in the sequence is a perfectly fair coin. Just the way we wanted. It should be intuitively