Recent content by Aryan1043

You're overcomplicating this. ##\overline{X}_n## is a continuous random variable so ##P(\overline{X}_n = a) = 0## for all ##a \in \mathbb{R}##. In particular $$\lim_{n \to \infty} P(\overline{X}_n = 2)= \lim_{n \to \infty} 0 = 0$$