Assume that \(X_{n}\stackrel{\mathbb{P}}{\to}X\) and that \(|X_{n}|\leq Y\) with \(\mathbb{E}[Y]<\infty\). Then \(\mathbb{E}[X_{n}] \to \mathbb{E}[X]\).
John Robin Inston
September 25, 2026
Assume that \(X_{n}\stackrel{\mathbb{P}}{\to}X\) and that \(|X_{n}|\leq Y\) with \(\mathbb{E}[Y]<\infty\). Then \(\mathbb{E}[X_{n}] \to \mathbb{E}[X]\).