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 −
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${[a,b]}$ = Interval in which x lies.
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${P(a \le X \le b)}$ = probability that some value x lies within this interval.
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${d_x}$ = 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: