Please answer the attached question

Problem 7 (15 pt): We denote by Fx(), FY(), Fz() the cdf (cumulative distribution function) of random variables X, Y, Z, respectively. Suppose that these random variables satisfy equality Elf ( X ) g (Y) h(Z)] = E[f(X)]E [g(Y)] E [h(Z) ] (4) for any functions f(), g(), h(). We are interested in proving that this fact implies statistical independence of X, Y, Z. For now, let us just prove that the above property implies Fx.y,z(1.0, 2.0, ") = Fx(1.0) Fy (2.0) Fz(*). (5) Specify functions f(), function g(), function h() that has properties: E[f(X)] = Fx(1.0) E[g(Y)] = FY (2.0) Eh(Z)] = Fz(*) E[f(X)g(Y)h(Z)] = Fx,y.z(1.0, 2.0, *). (9) For those specific functions f(), g(), h() that you specified, plot each of them against its independent variable. Justify your answers in detail