Let X1,X2, . . . be independent continuous random variables with a common distribution function F and density f = F, and suppose that they are to be observed one at a time in sequence. Let N = min{n  2: Xn = second largest of X1, . . . ,Xn}

and let M = min{n  2: Xn = second smallest of X1, . . . ,Xn}

Which random variable—XN, the first random variable which when observed is the second largest of those that have been seen, or XM, the first one that on observation is the second smallest to have been seen—tends to be larger?