How PDF works in continuous distribution?

Question

I'm very new in statistics. I was learning the PDF of Normal Distribution. But sometime before I learned that probability of getting exactly x in continuous distribution in 0. But what if I replace the value of x in PDF of normal distribution? It gives me the height and that is essentially the probability of getting x. So, probability of getting x is the height or the area in the distribution? If it is the area then what is the interpretation of the height?

I might have mixed concepts because this thing is not clear to me. It'll be great if you spare a few minutes to make me understand this. Thanks in advance.

Notice that probability densities do not have upper bound, so they can exceed 1, probabilities cannot. — Tim, Feb 27 '18 at 07:27

score 1 · Accepted Answer · answered Feb 27 '18 at 06:34

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The height you see in the continuous pdf is called 'density'. Similar to the usage in physics(mass per volume), we call it density because it is probability per measure. So in order to get a probability from the height, you should multiply it by some measure of $X$ (i.e. get the area / volume / ...). But relatively speaking, you can still compare densities of two different points to get, for example, odd ratio and stuff in a similar sense that you can say "Gold is heavier than water".

answered Feb 27 '18 at 06:34

Julius

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Plugging x in the formula of PDF returns the density? – lu5er Feb 27 '18 at 06:36
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yes. pdf(x) is the density at x. – Julius Feb 27 '18 at 06:40
And hence the name probability DENSITY function? – lu5er Feb 27 '18 at 06:44
That is correct. – Julius Feb 27 '18 at 06:45

How PDF works in continuous distribution?

1 Answers1