On some stochastic inequalities involving minimum of random variables

Let X_i be independent IFR random variables and let Y_i be independent exponential random variables such that EX_i]=EY_i] for all i=1, 2, ? n. Then it is well known that Emin (X_i)] ≥Emin (X_i)]. Nevertheless, for 1≤i≤n exponentially distributed X_i's and for a decreasing convex function ?(.). it is shown that .