Stochastic comparisons of random minima and maxima

Let X 1 , X 2 ,… be a sequence of independent random variables and let N be a positive integer-valued random variable which is independent of the X i . In this paper we obtain some stochastic comparison results involving min { X 1 , X 2 , …, X N ) and max{ X 1 , X 2 ,…, X N } .