Question: can I please get help with this question? Problem 6: Stationary Excess Let X be a non-negative random variable whose moments are all finite. Define

can I please get help with this question?

Problem 6: Stationary Excess Let X be a non-negative random variable whose moments are all finite. Define the ranomd variable Xe to have the stationary excess distribution of X if we have P(Xe s) ds. (0.4) Show the following: . X is an Exponential()) random variable if and only if X and Xe have the same distribution. . Find the distribution for Xe when X is constant. . If f is a differentiable function where Elf (x)] is well defined, then show that Elf(X) - f(0)] EX = Elf' (Xe)] (0.5) . Find a formula for Var[Xe] in terms of E[X], E[X2], E[X3]

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