Statistics 简明教程

Statistics - Probability Density Function

在概率论中，概率密度函数 (PDF) 或连续随机变量的密度是一个函数，描述了该随机变量取给定值的相对可能性。

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value.

概率密度函数由下式定义：

Probability density function is defined by following formula:

其中——

Where −

  1. ${[a,b]}$ = Interval in which x lies.

  2. ${P(a \le X \le b)}$ = probability that some value x lies within this interval.

  3. ${d_x}$ = b-a

Example

Problem Statement:

Problem Statement:

一天内，时钟在任意时间随机停止一次。如果停止的时间为 x，则 x 的 PDF 由下式给出：

During the day, a clock at random stops once at any time. If x be the time when it stops and the PDF for x is given by:

计算时钟在下午 2 点到下午 2:45 之间停止的概率。

Calculate the probability that clock stops between 2 pm and 2:45 pm.

Solution:

Solution:

我们已找到以下值的：

We have found the value of the following: