How do you show ? We know that . In other words, controls all the moments.

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- Jun 19th 2010, 01:07 PMSamprasprobability
How do you show ? We know that . In other words, controls all the moments.

- Jun 20th 2010, 07:09 AMtheodds
Try integration by parts, noting that where F is the CDF. Also, I think you are missing an assumption on the support of .

- Jun 20th 2010, 04:03 PMjamix
- Jun 21st 2010, 05:21 PMSampras
is non-negative.

So we know that . Let and . Then and . So

So we have:

and so the result follows. Is this correct?

- Jun 21st 2010, 05:27 PMSampras
Or more generally, one can show that using induction on ? One could use Markov's inequality: ?

- Jun 22nd 2010, 10:55 AMjamix
- Jun 22nd 2010, 02:58 PMawkward