Let be complex random variable. Prove that:
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Originally Posted by albi Let be complex random variable. Prove that: I'd start from the defintion: .
First of all we do not know if joint density for the variables exists. However I know (somebody told me) that it can be done in more abstract way using: 1. (for real variables) 2. Cauchy-Schwartz inequality But I don't know how....
Solution Let Than: Because we have Hence by Cauchy-Schwartz inequality (and expected value monotonicity)
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