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By Jensen’s inequality, Ef(X) ≥ f(EX) for any convex function f If f is twice differentiable and its second derivative is nonnegative, then f is convex For f(x) = xk, the second derivative is f00(x) = k(k −1)xk−2 which is nonnegative if x ≥ 0 2 (MU 27) Let X and Y be independent geometric random variables, where X has.
Fye xeue. Since 0 = u xy u x = (u y u) x, we can integrate at once with respect to xto obtain u yu= f(y)This is a rst order linear \ODE" in the variable y Introducing the integrating factor = exp R 1dy = ey, it becomes @y (e yu) = ef(y) Integrating with respect to ythis time yields. Shop The Falcon and The Winter Soldier Shop Anime Used.
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