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An identity on the maximum of a set of random variables

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  • Strait, Peggy Tang

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/[radical sign]2[pi])[1 + (1/[radical sign]2)].

Suggested Citation

  • Strait, Peggy Tang, 1974. "An identity on the maximum of a set of random variables," Journal of Multivariate Analysis, Elsevier, vol. 4(4), pages 494-496, December.
    • Handle: RePEc:eee:jmvana:v:4:y:1974:i:4:p:494-496
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    Cited by:

    1. Xu, Jian-Lun, 2014. "An identity on order statistics of a set of random variables," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 243-244.

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