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離散隨機變數的機率分配

The probability distribution or, simply the distribution of a discrete random variable X is a list of the distinct numerical values of Xalong with their associated probabilities. Often, a formula can be used in place of a detailed list.

Form of a Discrete Probability Distribution
$\begin{array}{cc} \hline \mbox{Value x}&\mbox{Probability f(x)} \\ \hline x_1&f... ...) \\ .&. \\ .&. \\ x_k&f(x_k) \\ \hline \mbox{Total}&1 \\ \hline \end{array}$

The probability distribution of a discrete random variable X is described as the function f(x_i)=P[X=x_i] which gives the probability for each value and satisfies:

1.: $f(x_i) \geq 0$ , for each value x_i of X.
2.: $\displaystyle\sum_{i=1}^k f(x_i)=1$

一般來講, 我們習慣用大寫字母 X 表示一個隨機變數及小寫字母 x表示隨機變數的一個值; f(x_i) 表示 X 中 x_i 值的機率, 在當隨機變數 X 其值僅為有限個可能或是可數無限的情況, 我門即稱為 離散型隨機變數.