Probability density

Question

I understand probability as the likelihood of something happening. I understand that a probability density function shows the probability that a random variable takes a range of values. But what exactly is the y axis of a pdf? I keep on seeing the phrase “probability per unit length” or equivalent, but what does the “per unit length” mean exactly?

edit: thank you all for your responses.

In: 3

Answer 1

A probability density function is an infinite regression of a count (y) to category (x) relationship, the categories being ranges of continuous values reduced so the actual range covered approaches zero (the regression), at which point the actual count becomes irrelevant.