Question: Let X,Y,Z>0 three random variables with distribution funcions Fx (x), Fy (y) and Fz(z). Let p 2 1 and II(X) = 6(1 F(x)). Show

Let X,Y,Z> 0 three random variables with distribution funcions Fx(x), Fy(y) and Fz(z). Let p > 1 and II(X) = f*(1 ? F(x))?. S

Let X,Y,Z>0 three random variables with distribution funcions Fx (x), Fy (y) and Fz(z). Let p 2 1 and II(X) = 6(1 F(x)). Show or give a counterexample (a random variable non- negative) of: II(X)=II(Y)=I(aX+(1-a)Z)=II(aY+(1a)Z). With 0 < a < 1. Note: EG[X] = II(X) with distribution G(x) = 1 (1 F(x)) with p > 1. Fax+(1-a)z(t) = aFx(1)+(1 a)Fz(t).

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