機率論快速學習05：隨機變量 二項分佈 泊松分佈

機率論快速學習05：隨機變量

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「不要在乎這些細節。」生活就是這樣,天天過的好一點.

 

Written In The Font

• 隨機變量

• 二項分佈

• 泊松分佈

• 泊松分佈與二項分佈的關係

Content

Random variable

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Random variable is usually understood to mean a real-valued random variable; this discussion assumes real values. A random variable is a real-valued function defined on a set of possible outcomes, the sample space Ω. That is, the random variable is a function that maps from its domain, the sample space Ω, to its range, the real numbers or a subset of the real numbers. It is typically some kind of a property or measurement on the random outcome.

                         

what is it? I think the definition is not clear to understand.In my words,Random variable can be used to describe the process of rolling dice and the possible outcomes.

 

Discrete probability distribution

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The range of distribution function is the discrete random variables, such as the onlyinteger is belongs to the discrete distribution.  represents the probability random variable  value. If the value of X is,then:

                       

 

Example:

若罰球兩次, 第一次罰中的機率爲0.75，若第一次罰中則第二次罰中的機率爲0.8，若第一次未罰中則第二次罰中的機率爲0.7.以X記罰球兩次其中罰中的次數，求X的分佈律。

解：X的可能取值爲0，1，2.

X	0	1	2
pk	0.075	0.325	0.6

 

也能夠經過一系列數據展示到圖上

                      

 

Binomial Distribution

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the binomial distribution is the discrete probability distributionof the number of successes in a sequence of n independent yes/no experiments.In general, if the random variable X follows the binomial distribution with parameters n and p, we writeX ~ B(n, p). The probability of getting exactly k successes in n trials is given by the probability mass function:

                       

Symbols for:

                     X～B (n, p)

 

show an example:

若某人作某事的成功率爲1%，他重複努力 400次，則至少成功一次的機率爲 :

                  

 

 

 

愛迪生: 「天才＝1%的靈感＋99%的汗水」 但那1%的靈感是最重要的，甚至比那99%的汗水都要重要

 

Poisson's distribution

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A discrete random variable X is said to have a Poisson distribution with parameter λ > 0, if, for k=0,1,2,…, the probability mass function of X is given by:

                 

Symbols for:

                  

 

The relation of binomial distribution and poisson's distribution

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when n –> ∞ , p < 0.1 :
                      

proved:

 

                    

 

Editor's Note

有些人不須要你去生氣,作好你本身.本身開心過好每一天,這樣就足夠了.