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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Originally Posted by Boysilver 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. Justify the following: (you may need independence and Cauchy-Schwarz inequality for the middle inequality)
I'd tried this briefly but hadn't considered using Cauchy Schwarz. This seems to give the result immediately - thanks!
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