松柏分佈是關于甚麼？

Poisson分佈（法語：loi de Poisson，英語：Poisson distribution，譯名有泊松分佈、普阿松分佈、卜瓦松分佈、布瓦松分佈、布阿松分佈、波以松分佈、卜氏分配等），是一種統計與機率學裡常見到的離散機率分佈，由法國數學家西莫恩·德尼·卜瓦松（Siméon-Denis Poisson）在1838年時發表。
卜瓦松分佈的機率質量函數為：


圖片參考：http://upload.wikimedia.org/math/9/f/a/9fa6dab1d04c709f1502cd54fdd43de7.png

卜瓦松分佈的參數λ是單位時間(或單位面積)內隨機事件的平均發生率。
卜瓦松分佈適合於描述單位時間內隨機事件發生的次數。如某一服務設施在一定時間內到達的人數，電話交換機接到呼叫的次數，汽車站台的候客人數，機器出現的故障數，自然災害發生的次數等等。
網上好難找中文例題﹐以下是幾條英文題
Example 1: Mr. Wildman has done a study to determine the number of students that attend office hours. After studying the problem over one month, he determines that on average two students arrive for every office hour he schedules. Find the probability that for a randomly selected office hour, the number of student arrivals is:
a. 0
b. 2
c. 5
d. 9
Solution: Poisson applies since the distribution is over a given time period (an office hour). The mean as stated in the problem is 2. So using the formula:


圖片參考：http://wind.cc.whecn.edu/~pwildman/statnew/new_pa24.gif

Example 2: A trucking company operates a large fleet of trucks and last year they had 103 breakdowns. Find the mean number of breakdowns per day and the probability on any given day you have 2 breakdowns or say at least 2 breakdowns
Solution: You had 103 breakdowns all year and so the mean number of breakdowns per day is 103/365 = .282. Using Poisson - you get
P(2) =
圖片參考：http://wind.cc.whecn.edu/~pwildman/statnew/new_pa29.gif

Example 3: If you bet a 7 on a roulette wheel there is a probability of 1/38 of winning. Assume bets are placed on the number 7 in each of 500 different spins
Solution: The mean number of wins is n x p = 500 x 1/38 = 13.2 according to the binomial distribution
We use Poisson to get the probability that 7 occurs exactly 13 times

圖片參考：http://wind.cc.whecn.edu/~pwildman/statnew/new_pa30.gif