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I have difficulties in solving following problem in Rick Durrett's "Probability Theory and Examples"

This is the problem 2.3.15 in the 4th edition and problem 1.6.15 in the 3rd edition:

Let $Y_1$, $Y_2$, ... be i.i.d. Find necessary and sufficient conditions for (i) $Y_n/n \to 0$ almost surely, (ii) $(\max_{m\leq n}Y_m)/n\to 0$ almost surely, (iii) $(\max_{m\leq n}Y_m)/n\to 0$ in probability, (iv) $Y_n/n \to 0$ in probability.

I can't figure out question (ii) and (iv). Any hint will be appreciated.

Tianyi Jia
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1 Answers1

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Hint: if a sequence converges, then every sub-sequence converges. Also, convergence almost surely implies convergence in probability.