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The probability density function is nonnegative everywhere, and its integral over the entire space is equal to one. The area under the graph is the area of a rectangle. More generally, if the density has a large value over a small region, then the probability is comparable to the value times the size of the region. I say "comparable to" rather than "equal to" because the value my not be the same at all points in the region.

## Your Answer

Density means probability per unit value of the random variable. If we know a PDF function e. To find the probability that the output of a random event is within some range, you integrate the PDF over this range.

Also see Why mvnpdf give probablity larger than 1?

## We need you!

I would like to point out an extreme example. It will be the same. So the bottom line here.

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Consider a probability density function of some continuous distribution. Why it is called density function?? Unlikely the probability mass function of a discrete distribution p. Conventionally probability of a point is considered as '0' for continuous distribution.

## Description

Then comes the question what actually does p. Now the physical interpretation of density is ratio of mass and volume of a substance. Here probability density function is similarly the mass which is similar to the frequency and the volume which is similar to the field of experiment ratio.

This only holds for discrete random variables. Home Questions Tags Users Unanswered. How can a probability density be greater than one and integrate to one Ask Question.

Asked 7 years, 11 months ago.

## ... Or Equal To ...

Active today. Viewed 72k times. How are these two things compatible? Zev Chonoles k 16 16 gold badges silver badges bronze badges.

Is it 1? If you take a fixed mass of liquid and compress certain parts of it, you can make the local density as high as you like without changing the total mass.

Michael Hardy Michael Hardy k 24 24 gold badges silver badges bronze badges. Zaz 1 1 gold badge 11 11 silver badges 27 27 bronze badges.

Yang Zhou Yang Zhou 3 3 silver badges 3 3 bronze badges. For continuous probabilities it only makes sense to talk about probabilities near a point. Sathyam Sathyam 2 2 silver badges 8 8 bronze badges. So, it can be more than one and it can be anything.

## Equal, Greater or Less Than

For further discussion please ask me through gmail. Sutanu Sardar Sutanu Sardar 9 1 1 bronze badge.

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We get probabilities from a pdf by integrating. In fact, a pdf can be unbounded. Mauve 1, 3 3 gold badges 6 6 silver badges 17 17 bronze badges. Shubham Kothawade Shubham Kothawade 1.

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## Greater Than

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