題組內容

1. Let $\{Xn, n \ge 1\}$ and $\{Yn, n \ge 1\}$ be sequences of random variables and $X$ and $Y$ be random variables. Please indicate whether the following statements are true or false. If a statement is false, explain why. (30%)

(f) If $Xn \to X$ in probability, then $Xn \to X$ almost surely.