An identity on the maximum of a set of random variables

Peggy Tang Strait

Journal of Multivariate Analysis, 1974, vol. 4, issue 4, 494-496

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)].

Keywords: Maximum; of; a; set; of; random; variables; expectation; symmetric; random; variables; independent; identically; distributed; random; variables; standard; normal; random; variables (search for similar items in EconPapers)
Date: 1974
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Citations: View citations in EconPapers (1)

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