Does $|X_n|\le\Delta_n+\delta$, with $\Delta_n\overset{p}\to0$ imply $|X_n|\overset{p}\to0$?

by J.Mike   Last Updated May 15, 2019 18:20 PM

Suppose $\Delta_n\overset{p}\to0$, and for any $\delta>0$, we have $$|X_n|\le\Delta_n+\delta.$$

Can we conclude that


Here $\Delta_n\overset{p}\to0$ means that for any $\varepsilon>0$, we have $\lim_{n\to\infty}P(|\Delta_n|>\varepsilon)=0$.

Related Questions

Questions on Showing $X_{n}Y_{n}\xrightarrow{P} XY$

Updated January 09, 2019 23:20 PM

Limit of multinomial distributions

Updated November 29, 2017 23:20 PM