law of large numbers

Printable View

February 12th 2011, 11:39 AM
slavert

law of large numbers

Let $X_{1},...,X_{n}$ be independent random variables, that
$P(X_{i}=1)=1/i=1-P(X_{i}=0)$ and $K_{n}=X_{1}+...+x_{n}$
Show that $K_{n}/log(n) to1$ with probability
Decide if $K_{n}/log(n) to 1$ almost sure
Hint $\frac{sum_{k=1}^{n}1/k}{log(n)}\arrow$

Thx for any help

All times are GMT -8. The time now is 05:31 PM.

Copyright © 2005-2013 Math Help Forum. All rights reserved.

Copyright © 2005-2013 Math Help Forum. All rights reserved.