Statistics 简明教程

Statistics - Cumulative Poisson Distribution

${\lambda}$ 是形狀參數，表示給定時間間隔內的事件平均數。以下是四個 ${\lambda}$ 值的泊松機率密度函數的繪圖。累積分佈函數。

${\lambda}$ is the shape parameter which indicates the average number of events in the given time interval. The following is the plot of the Poisson probability density function for four values of ${\lambda}$. Cumulative Distribution Function.

cumulative poisson distribution

Formula

其中——

Where −

  1. ${e}$ = The base of the natural logarithm equal to 2.71828

  2. ${k}$ = The number of occurrences of an event; the probability of which is given by the function.

  3. ${k!}$ = The factorial of k

  4. ${\lambda}$ = A positive real number, equal to the expected number of occurrences during the given interval

Example

Problem Statement:

Problem Statement:

一個複雜的軟體系統平均每 5,000 行程式碼有 7 個錯誤。從 5,000 行隨機選擇的程式碼行中，恰好有 2 個錯誤的機率是多少？

A complex software system averages 7 errors per 5,000 lines of code. What is the probability of exactly 2 errors in 5,000 lines of randomly selected lines of code?

Solution:

Solution:

從 5,000 行隨機選擇的程式碼行中，恰好有 2 個錯誤的機率是：

The probability of exactly 2 errors in 5,000 lines of randomly selected lines of code is: