- Let be independent random variables with . Set . Then
*Proof:*LetNotice that and

- If also , then
*Proof:*Notice thatand thus

Combining the above result and 1 we have

and hence

Advertisements

- Let be independent random variables with . Set . Then
*Proof:*LetNotice that and

- If also , then
*Proof:*Notice thatand thus

Combining the above result and 1 we have

and hence

Advertisements

This entry was posted in Inequalities, Statistics and tagged Inequality, Kolmogorov, Probability. Bookmark the permalink.

%d bloggers like this: