If X and Y are two independent identically distributed real valued random variables, show that

.

Here's the hint: For let and let

and

.

Draw and compare these sets and use independence.

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- November 15th 2009, 08:20 AMBoysilverVery nice (but quite tough) puzzle
If X and Y are two independent identically distributed real valued random variables, show that

.

Here's the hint: For let and let

and

.

Draw and compare these sets and use independence. - November 15th 2009, 10:45 AMLaurent
- November 15th 2009, 12:25 PMBoysilver
I'd tried this briefly but hadn't considered using Cauchy Schwarz. This seems to give the result immediately - thanks!