An identity on the maximum of a set of random variables
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)].
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Volume (Year): 4 (1974)
Issue (Month): 4 (December)
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