泊松分布

题目

泊松分布
The number of defective components produced by a certain process follows
a Poisson distribution with mean k.Each defective component has probability p0 as being
repairable.
a.Find the probability that exactly N defective components are found.
b.Suppose we have exactly N defective components,let Y be the number of repairable
components,ˉnd the probability distribution of Y .
c.Find the moment generating function of the distribution you obtained in part b.
d.What is the probability that we ˉnd exactly N defective components,and among them,
n are repairable?

答案

a: exp(-k)*N^k/N! (感叹号表示阶乘)b：Y服从B(N,p0) (二项分布)c:矩母函数：（1-p0+p0*exp(t)）^Nd:这是个复合泊松过程,每一项是两点分布, 可以修复的元件的个数的剧目函数是exp{K（1-p0+p0*exp(t)）^N)-1} 期望...