Probability density function

The range (spread of values of x) is plotted horizontally. The probability is plotted vertically and cannot exceed 1.0.

Thank you for your reply. However, I do get the differente between x and f(x). what I don't get is the following:

the PDF of a Normal distribution is exp[-(x-mu))^2/2*sigma^2] / [sigma*sqrt(2*pi)]

with mu= and sigma=0.2, for x=0, it becomes:

f(x) = 1/[0.2*sqrt(2*pi)] = 1.99

how can it be higher than 1?

The density function can be greater than one, the integral of the PDF over a finite range will not be.

https://en.wikipedia.org/wiki/Probability_density_function#Further_details

Let's imagine a function where there are no values less than 0.4 and no values greater than 0.6. All the values are between those two points.

The PDF is
0 for x < 0.4
5 for 0.4 < x < 0.6
0 for x > 0.6

So, WOW, THE PDF IS 5! But only over a short range. If you integrate the entire PDF over x from 0 to 1, you get 100%. If you integrate the PDF from 0.5 to 0.6, you get 5 x 0.1 = 50%. Even though the PDF is greater than one, the integral is not.

Thanks. So, to come back to my original question, what is the meaning of PDF? It's not "the likelihood that x can assume a specific value" because then a PDF>1 should be impossible.

The probability function is "the likelihood that x can assume a specific value". The probability density function is a function you can use to compute the probability over a certain range of values. It is the derivative of the probability function. That is why it can be greater than one.