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
Probability density is a mathematical tool to help calculate actual probabilities.
The y-axis is the thing it needs to be for the probability density function to work. It doesn’t really have meaning on its own.
The “probability per unit length” thing comes from working backwards – as does probability density itself.
The area under a probability density function gives us a probability. Area has dimensions of length * height, so if:
> length * height = probability
> height = probability / length
So in this case “length” is whatever your x-axis is.
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