Hello,

For ii) the reverse way, use Borel-Cantelli lemma 2, since you have the independence of the random variables.

If you don't know it, just find a proof for the second part of Borel-Cantelli lemma on the internet !

And to answer your first question, have a look here : http://www.mathhelpforum.com/math-he...ty-116269.html

it may be helpful for you to read the thread, and you may find the way to prove i) : there is no need to use Chebyshev !