Definition: A sequence of random variables \(\x_n\) is bounded in probability if for any \(\eps > 0\), there exist \(M\) and \(N\) such that \(\Pr\{\norm{\x_n} > M\} < \eps\) for all \(n > N\).
Definition: A sequence of random variables \(\x_n\) is bounded in probability if for any \(\eps > 0\), there exist \(M\) and \(N\) such that \(\Pr\{\norm{\x_n} > M\} < \eps\) for all \(n > N\).