Convergence, Probability, Cumulative Distribution, Statistics, Editors Pick.
X ~ Bernoulli(0.5). Thus, the sequence X_1, X_2, …, X_n converges in distribution to X. But does it converge in probability to X? It turns out, it doesn’t. Like two different coins, X_n and X are two independent Bernoulli random variables. We saw that when n tends to infinity, X_n turns into a