Random Variables

[Steven G]

All I can see in this problem is that E(X_i) = 0 and p(a<X_i<b) = (b-a)/(2i) assuming (a,b) is in [-i,i].
Please help. Thanks!

 

[Cubist]

This might be the wrong direction to go in, but maybe start by considering the sum of two uniform distributions only and then maybe it can be extended to the sum of n somehow...

Convolution of probability distributions - Wikipedia

en.wikipedia.org

 

[Romsek]

according to the central limit theorem what is the limiting distribution of all sums of IID random variables?

 

[Romsek]

deleted for now