求解Poisson分布和二项分布高阶矩的代数方法

Algebraic Method of Solving Nth Moment of Poisson and Binomial Distribution

给出了求解Poisson分布和二项分布高阶矩的一种代数方法,避免了计算无穷级数的不便和误差。证明了xn可以表为连续的一次因式的乘积的和,并给出了求解系数的二种方法:待定系数法和余数法;编程求解了前10个幂的表出系数。得到了Poisson分布和二项分布高阶原点矩的代数求解公式。

We have given an algebraic method of solving the Nth moment of the poisson and the binomial distribution, so that the error can be avoided.The continuous product of one degree factor standing for x^n was proved,with two methods proposed to find coefficients:one being undermined;the other being remainder number.The solution to 10th power series expansion was found through programming.Thus,algebraic method to solve Nth moment of poisson and binomind distribution was obtained.