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.

Formula
其中——
Where −
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${e}$ = The base of the natural logarithm equal to 2.71828
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${k}$ = The number of occurrences of an event; the probability of which is given by the function.
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${k!}$ = The factorial of k
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${\lambda}$ = 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: