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$\dfrac{\max|X_i|}{n}$ tends almost surely to $0$ where '$X_i$' has a distribution with finite $2$nd order moments. Can anyone here provide me with the proof?

Michael Hardy
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Dwaipayan Gupta
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  • Do you mean that ALL of the $X_i$ have bounded second order moments where there is a universal bound on the second moments, i.e. all second moments are less than $M$ for some $M > 0$? – user2566092 Aug 05 '15 at 18:15
  • Also, it would make it easier if all your $X_i$ were independent identically distributed. Is that the case? – user2566092 Aug 05 '15 at 18:19
  • yes and yes.

    the replies to both of your questions. @user2566092

     – Dwaipayan Gupta Aug 05 '15 at 18:34
  • We're here to provide you with help for your own learning and understanding (as opposed to providing you with proofs). What part of the problem are you stuck at? For starters, can you write down the definition of a sequence of random variables tending almost surely to $0$? – Greg Martin Aug 05 '15 at 18:37
  • yes and yes. the replies to both of your questions. @user2566092 – Dwaipayan Gupta Aug 05 '15 at 18:34

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