machine-learning - 正态分布连续变量的概率计算

Question

我看到一个公式来计算所附图像中任何值(x=x1)的概率。任何连续变量对于特定值的概率不是为零吗？因为概率就是面积对吗？这是在 2 个值之间计算的。那么，对于任何特定的连续值，概率不都是 0 吗？如果我错了，请有人纠正我!

Answer 1

你是对的。连续分布中任何特定值的概率为零。您发布的方程不是概率公式，而是 Probability Density Function 的公式

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample. In other words, while the absolute likelihood for a continuous random variable to take on any particular value is 0 (since there are an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer that, in any particular draw of the random variable, how much more likely it is that the random variable would equal one sample compared to the other sample.