乘数原理multiplication.ppt

Probability Distribution A mathematical model that relates the value of the variable with the probability of occurrence of that value in the population.
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Important Discrete Distributions Fundamentals of Probability and Statistics
The Hypergeometric Distribution The Binomial Distribution The Poisson Distribution The Pascal and Related Distributions
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Hypergeometric Distribution
Fundamentals of Probability and Statistics
The Hypergeometric distribution is
D ND
x n x
p(x) N
nD
N
n
2
nD N
Fundamentals of Probability and Statistics
乘數原理(multiplication principle)
假設一試驗E1有n1種可能結果，對此n1個 可能結果進行另一試驗E2，又有n2可能結 果，則此組合試驗E1-E2，共有n1n2可能 結果。
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distribution if
X
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1 (success) with probability p 0 (failure) with probability 1-p
1
D N
Nn N 1
N：母體數； D：某特定類別之物品數； n：樣本數 x：抽出n個物品中正好有x個是屬於D類之個數
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Example
Fundamentals of Probability and Statistics
有100支保險絲，隨機抽5支，若在某電壓 下均燒斷，則接受。若已知該批有20支不 良保險絲，則允收機率為何?
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Bernoulli trial
Fundamentals of Probability and Statistics
An experiment with two, and only two, possible
outcomes. A random variable X has a Bernoulli(p)
Distributions
Fundamentals of Probability and Statistics
Continuous When a variable being measured is expressed on a continuous scale, its probability distribution is called a continuous distribution. The probability distribution of piston-ring diameter is continuous.
Random Variable variable that can take on different values in the population according to some “random” mechanism.
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Two Types of Probability
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問題2
Fundamentals of Probability and Statistics
汽車牌照號碼前兩碼可為英文字母或數 字，後四碼可為數字。試問此設計共可 容納多少車輛?
六個學生要坐一排有10張椅子的座位上， 有多少種不同坐法?
自生產線上抽出10個產品檢驗，其中檢 查出三個不良品。然而此三個不良品可 能是第1、2、3個，也有可能是第2、5、 8個…。試問共有多少種可能情況?
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Probability Distributions
Definitions
Fundamentals of Probability and Statistics
Sample A collection of measurements selected from some larger source or population.
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問題1
Fundamentals of Probability and Statistics
某西餐廳推出系列套餐組合，第一道湯品 共有5種，第二道沙拉共有4種，第三道主 菜共有10種，最後附餐則有5種。試問此系 列套餐共有幾種搭配方式?
某公司推出兒童電子琴玩具，其中有兩個 可撥0~9的數字鍵，此兩鍵任意撥一號碼即 發一種特殊音效，試問此玩具共可發出多 少種音效?
Discrete When the parameter being measured can only take on certain values, such as the integers 0, 1, 2, …, the probability distribution is called a discrete distribution. The distribution of the number of nonconformities would be a discrete distribution.
1
n個事物中取r個之四種情況
Fundamentals of Probability and Statistics
抽出不放回
抽出放回
考 慮 順
n
n! r
!
Prn
nr
序
(permutation)
不 考 慮
n
n!
r!r
!
Cnr
順
序
(combination)
C n r 1 r
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