Statistics 简明教程

Statistics - Continuous Uniform Distribution

连续均匀分布是指在 a 和 b 之间的连续时间间隔内随机选择数的概率分布。其密度函数由以下公式定义。以下为 a = 1 和 b = 3 时的连续均匀分布图。

The continuous uniform distribution is the probability distribution of random number selection from the continuous interval between a and b. Its density function is defined by the following. Here is a graph of the continuous uniform distribution with a = 1, b = 3.

Formula

Example

Problem Statement:

假设你正在做一个测试，向 20 个竞赛者提出了一个问题。回答该问题的时间限制是 30 秒。有多少人在 5 秒内可能会作出反应？（通常，竞赛者需要点击一个按钮做出正确决定，根据第一个反应选择冠军。）

Suppose you are leading a test and present an inquiry on the crowd of 20 contenders. The time permitted to answer the inquiry is 30 seconds. What number of persons is prone to react inside of 5 seconds? (Regularly, the contenders are required to click a catch of the right decision and the champ is picked on the premise of first snap).

Solution:

步骤 1：概率分布的时间区间为 [0, 30]。

Step 1: The interval of the probability distribution in seconds is [0, 30].

⇒ The probability density is = 1/30-0=1/30.

步骤 2：要求的是在 5 秒内会答题的人数。也就是，成功事件子区间为 [0, 5]。现在，概率 P(x < 5) 是这两个区间宽度的比例。

Step 2: The requirement is how many will respond in 5 seconds. That is, the sub interval of the successful event is [0, 5]. Now the probability P (x < 5) is the proportion of the widths of these two interval.

⇒ 5/30=1/6.

由于有 20 个竞赛者，因此在 5 秒内可能会作出反应的竞赛者数量为 (1/6) (20) = 3。

Subsequent to there are 20 contenders, the quantity of contenders prone to react in 5 seconds is (1/6) (20) =3.