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
It’s basically probability per some section of the graph. So in practice, let’s say you had probability density function that represented people’s heights. Let’s you want to find the odds that a person is 180 cm tall. In practice, the odds of that are practically 0, because you would need to be 180 to a microscopic degree. You can’t be 180.0000000001 or 179.999999999. So you normally don’t work with exact values, you work with ranges. So let’s say you wanted to know the odds that someone is between 179.5 cm tall and 180.5. Height would be the X axis, and if you take that section of the probability density function between 179.5 and 180.5 and calculated the area, that would be the odds that your height is between 179.5 and 180.5.
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