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MATH2036 COMPLEX FUNCTIONS FINAL EXAM A LEVEL 2 MODULE, 2021-2022Problem 1. (A) A Set A ⊂ C Is Called Convex If ∀X, Y ∈ A And ∀Λ ∈ [0, 1] [12 Marks](1 − Λ)X + Λy ∈ A.Show That If Domains An, N = 1, 2, . . . Are Convex And ∩∞N=1An = ∅ Then The Set ∪∞N=1An Is A Starshape-Domain.(B) Let The Function F

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Nonparametric Econometrics Problem Set 1 Due March 12, 2024 Exercises 1. The Kernel Density Estimator Is Defined Aswhere X1, X2, . . . , Xn Are Iid Observations. If The Kernel Function K(·) Satisfies That ( I ) ∫ K(U)Du = 1; ( Ii ) K(U) = K (−U); ( Iii ) ∫ U2k(U)Du = Κ2 &< ∞, Prove That2. In Our Lec