Let X,Y,Z>0 three random variables with distribution funcions Fx (x), Fy (y) and Fz(z). Let p...

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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+(1–a)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). 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+(1–a)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).