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泊松分布
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泊松分布
1.
2.
一、泊松分布的定义及图形特点 设随机变量 X
所有可能取的值为 0 , 1 , 2 , … , 且概率分布为: 其中 >0 是常数 , 则称 X 服从参数为 的 泊松分布 , 记作 X ~ P ( ).
3.
历史上,泊松分布是作为二项分布的近似,于 1837 年由法国数学家泊松引入的
. 近数十年来, 泊松分布 日益显示 其重要性 , 成为概率论中最重要的几个分布之一 . 在实际中,许多随机现象服从或近似服从泊松分布 . 二项分布与泊松分布
4.
某电话交换台在一段时间内收到的电话呼叫数; 一个售货员接待的顾客数 ;
公共汽车站在一段时间内来到的乘客数等等 都近似服从泊松分布。 一、社会生活对服务的各种要求
5.
放射性分裂落在某区域的质点数,热电子的发射 显微镜下落在某区域中的血球或微生物的数目 二、物理学和生物学领域
一放射性源放射出的 粒子数;
6.
三、有泊松定理知,泊松分布可以作为描绘大量试验中 稀有事件 出现的频率的概率分布的数学模型。
7.
由泊松定理, n 重贝努里试验中
稀有事件 出现的次数近似地服从泊松分布 . 我们把在每次试验中出现概率很小的事件称作 稀有事件 . 如地震、火山爆发、特大洪水、意外事故等等
8.
到某机场降落的飞机数 ; 纱锭的纱线被扯断的次数;
一页中印刷错误出现的数目; 一年中暴雨出现在夏季中的次数; 三胞胎出生的次数; 数字通讯中传输数字时发生误码的个数等等
9.
在自然界和人们的现实生活中 , 经常要遇到在随机时刻出现的某种事件
. 我们把在随机时刻相继出现的事件所形成的序列 , 叫做随机事件流 . 若事件流具有平稳性、无后效性、普通性,则称该事件流为泊松事件流( 泊松流 ) . 泊松分布产生的一般条件 下面简要解释 平稳性、无后效性、普通性 .
10.
平稳性 : 在任意时间区间内,事件发生
k 次 ( k ≥0) 的 概率只依赖于区间长度而与区间端点无关 . 无后效性 : 普通性 : 在不相重叠的时间段内,事件的发生是相 互独立的 . 如果时间区间充分小,事件出现两次或两次以上的概率可忽略不计 .
11.
都可以看作泊松流 . 某电话交换台收到的电话呼叫数;
到某机场降落的飞机数 ; 一个售货员接待的顾客数 ; 一台纺纱机的断头数 ; … 例如 一放射性源放射出的 粒子数;
12.
对泊松流, 在任意时间间隔 (0,
t ) 内 , 事件 ( 如交通事故 ) 出现的次数服从参数为 t 的 泊松分布 . 称为泊松流的强度 .
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