Let \(X_1,X_2,\ldots \) be i.i.d. with \(\mathbb {P}(X_1>x)=e^{-x}\), \(x>0\). Prove that \[ \limsup _{n\to \infty } \frac {X_n}{\ln n}=1 \] a.s.
Question
Math 6010 • Linear Models
Spring 2008 • Question 8
Question
Spring 2008 • Question 8
Let \(X_1,X_2,\ldots \) be i.i.d. with \(\mathbb {P}(X_1>x)=e^{-x}\), \(x>0\). Prove that \[ \limsup _{n\to \infty } \frac {X_n}{\ln n}=1 \] a.s.