Given mean and variance of a Gaussian (normal) random variable, I would like to compute its probability density function (PDF).
I referred this post: Calculate probability in normal distribution given mean, std in Python,
Also the scipy docs: scipy.stats.norm
But when I plot a PDF of a curve, the probability exceeds 1! Refer to this minimum working example:
import numpy as np
import scipy.stats as stats
x = np.linspace(0.3, 1.75, 1000)
plt.plot(x, stats.norm.pdf(x, 1.075, 0.2))
plt.show()
This is what I get:
How is it even possible to have 200% probability to get the mean, 1.075? Am I misinterpreting anything here? Is there any way to correct this?
It's not a bug. It's not an incorrect result either. Probability density function's value at some specific point does not give you probability; it is a measure of how dense the distribution is around that value. For continuous random variables, the probability at a given point is equal to zero. Instead of p(X = x), we calculate probabilities between 2 points p(x1 < X < x2) and it is equal to the area below that probability density function. Probability density function's value can very well be above 1. It can even approach to infinity.
来源：https://stackoverflow.com/questions/38141951/why-does-scipy-norm-pdf-sometimes-give-pdf-1-how-to-correct-it