Solve the following problem:
When a cdf F(x) has a tail power of α (i.e., when 1 - F(x) ∝ x-α for x large enough):
a. Show that E[X|X>K] = Kα/(α - 1) for K large enough. Discuss the existence of this expectation as a function of α.
b. Derive an estimate of E[X|X>K] based on a sample from F.
c. Evaluate the stability of this estimate as a function of K when F is a Pareto P(2), P(3), P(4) distribution.