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An identity on the maximum of a set of random variables |
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| Authors: | Peggy Tang Strait |
| Affiliation: | Queen''s College of the City University of New York USA |
| Abstract: | It is shown that if X1, X2, …, Xn are symmetric random variables and max(X1, …, Xn)+ = max(0, X1, …, Xn), then E[max(X1,…,Xn)+]=[max(X1,X1,+X2,+X1,+X3,…X1,+Xn)+], and in the case of independent identically distributed symmetric random variables, E[max(X1, X2)+] = E[(X1)+] + (1/2)E[(X1 + X2)+], so that for independent standard normal random variables, E[max(X1, X2)+] = (1/√2π)[1 + (1/√2)]. |
| Keywords: | Maximum of a set of random variables expectation symmetric random variables independent identically distributed random variables standard normal random variables |
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