The correlation coefficient between the smallest and largest observations when (N-1) of the n observations are iid exponentially distributed
Alan J. Gross, Hurshell H. Hunt, Robert E. Odeh · Communication in Statistics- Theory and Methods · 1986
A random sample of size n is obtained from two exponential populations in the following manner: (n-1) observations are selected from one of these populations and a single observation is selected from the other population. The correlation coefficient for Y1and Yn, the first and n-th order statistics is obtained. More ngenerally, it is shown in the course of the derivation that Yj-Yi is independent of YK-Y1 for all i, j, l and k such that I < j < l < k. This result is weil known when all the observations are iid exponentially distributed.