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In mathematics, the Schuette–Nesbitt formula is a generalization of the inclusion–exclusion principle. It is named after Donald R. Schuette and Cecil J. Nesbitt. The probabilistic version of the Schuette–Nesbitt formula has practical applications in actuarial science, where it is used to calculate the net single premium for life annuities and life insurances based on the general symmetric status. ==Combinatorial versions== Consider a set and subsets . Let denote the number of subsets to which belongs, where we use the indicator functions of the sets . Furthermore, for each , let denote the number of intersections of exactly sets out of , to which belongs, where the intersection over the empty index set is defined as , hence . Let denote a vector space over a field such as the real or complex numbers (or more generally a module over a ring with multiplicative identity). Then, for every choice of , c_n = \sum_^m N_k\sum_^k (-1)^\binom klc_l,|}} where }} denotes the indicator function of the set of all with , and is a binomial coefficient. Equality () says that the two -valued functions defined on are the same. Proof of () 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Schuette–Nesbitt formula」の詳細全文を読む スポンサード リンク
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