Why are the following two statements about convergence in probability the same. Probably a silly question, but I don't see the direct link

$$P(|X_n| > \delta) \rightarrow 0$$


$$P(|X_n| > M) < \epsilon $$

for sufficiently large $n$, where $\epsilon$, $\delta$ and $M$ are some positive constants.

  • 1
    $\begingroup$ This is not really about convergence in probability but about different formulations of the limit of a sequence. $\endgroup$ – Calculon Oct 18 '18 at 20:01

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