離散型均匀分布

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**離散型均匀分佈**
-{A\|zh-cn:概率;zh-tw:機率}-質量函數 n=5 where n=b-a+1
累積分佈函數 n=5 且 n=b-a+1. The convention is used that the cumulative mass function $F k (k i)$ is the probability that k > = ki
參數	$a \in (...,-2,-1,0,1,2,...)\,$ $b \in (...,-2,-1,0,1,2,...)\,$ $n=b-a+1\,$
Support	$k \in \{a,a+1,...,b-1,b\}\,$
-{A\|zh-cn:概率質量函數;zh-tw:機率質量函數}-	$\begin{matrix} \frac{1}{n} & \mbox{for }a\le k \le b\ \\0 & \mbox{otherwise } \end{matrix}$
累積分佈函數	$\begin{matrix} 0 & \mbox{for }k<a\\ \frac{k-a+1}{n} & \mbox{for }a \le k \le b \\1 & \mbox{for }k>b \end{matrix}$
期望值	$\frac{a+b}{2}\,$
中位數	$\frac{a+b}{2}\,$
眾數	N/A
方差	$\frac{n^2-1}{12}\,$
偏度	$0\,$
峰度	$-\frac{6(n^2+1)}{5(n^2-1)}\,$
信息熵	$\ln(n)\,$
動差生成函數	$\frac{e^{at}-e^{(b+1)t}}{n(1-e^t)}\,$
特性函数	$\frac{e^{iat}-e^{i(b+1)t}}{n(1-e^{it})}\,$

在統計學及概率理論中，離散型均匀分佈是一個離散型概率分佈，其中有限個數值擁有相同的概率。

A random variable that has any of $n$ possible values $k_1,k_2,\dots,k_n$ that are equally probable, has a discrete uniform distribution, then the probability of any outcome $k i$ is $1 / n$ . A simple example of the discrete uniform distribution is throwing a fair die. The possible values of $k$ are 1, 2, 3, 4, 5, 6; and each time the die is thrown, the probability of a given score is 1/6.

In case the values of a random variable with a discrete uniform distribution are real, it is possible to express the cumulative distribution function in terms of the degenerate distribution; thus

$F(k;a,b,n)={1\over n}\sum_{i=1}^n H(k-k_i)$

where the Heaviside step function $H (x - x 0)$ is the CDF of the degenerate distribution centered at $x 0$ . This assumes that consistent conventions are used at the transition points.

See rencontres numbers for an account of the probability distribution of the number of fixed points of a uniformly distributed random permutation.

来自“http://zh.wikipedia.org../../../%E9%9B%A2/%E6%95%A3/%E5%9E%8B/%E9%9B%A2%E6%95%A3%E5%9E%8B%E5%9D%87%E5%8C%80%E5%88%86%E5%B8%83.html”

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