Difference between a PDF and PMF

Question

What is the difference between a probability density function and a probability mass function?

Does this answer your question? Probability density function vs. probability mass function — , Jan 01 '22 at 05:30

score 4 · Accepted Answer · edited Apr 01 '22 at 05:55

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One is for discrete variables, the other for continuous.

They are also interpreted differently. The PDF is a probability density. If f(x) is a PDF, f(x) doesn't tell you the probability of getting x (In fact, the probability of getting precisely x is 0). The way you use a PDF is through integration. So, the probability of getting a value that is in a dx area around x is approximately f(x)*dx.

edited Apr 01 '22 at 05:55

Hossein Naghdbishi

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answered Mar 07 '14 at 00:32

elexhobby

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why is it approximate? What is an exact value? $f(x)dx + o(dx^2)$? – Naz Mar 24 '19 at 12:44
Can discrete random variables can be treated as continuous (and thus be described by a PDF as well)? – ryanwebjackson Mar 08 '22 at 03:49

score 3 · Answer 2 · answered Mar 07 '14 at 00:25

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To be precise, a probability mass is a probability distribution. However, it is not a probability density - probability masses are discrete, while probability densities are continuous.

answered Mar 07 '14 at 00:25

Ayesha

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So the only difference is that a PDF is continuous? – Deekor Mar 07 '14 at 00:28
More or less. Keep in mind that the discrete-ness of a PMF gives rise to some other differences. For example, the value of a PMF for an element of the sample space is a probability, while we must integrate the PDF to obtain a probability. – Ayesha Mar 07 '14 at 00:30

Difference between a PDF and PMF

2 Answers2