 # Density (of Probability)

Density Functions:

A probability density function or curve is a non-negative function ( ) that describes the distribution of a continuous random variable . If is known, then the probability that a value of the variable is within an interval is described by the following integral

For very small intervals , where is a small value, the relation is simpler:

The reason for using probability density instead of probability itself is the following: Continuous variables, in contrast to discrete random variables cannot be described by the probability of particular values of because there are infinitely many possible values and they are not countable. This makes the probability of any particular value equal to zero. For example, the probability that the body weight of an individual is exactly kilogram is practically zero, but the probability that body weight is within the interval kg is a measurable quantity.

Note that the probability density function is the curve itself, and the probability is the area under the curve.

See also: joint probability density , marginal density , and short course Basic Concepts in Probability and Statistics.

Browse Other Glossary Entries

## Test Yourself

Planning on taking an introductory statistics course, but not sure if you need to start at the beginning? Review the course description for each of our introductory statistics courses and estimate which best matches your level, then take the self test for that course. If you get all or almost all the questions correct, move on and take the next test.

### Data Analytics

Considering becoming adata scientist, customer analyst or our data science certificate program?

Analytics Quiz

Statistics Quiz

### Statistics

Looking at statistics for graduate programs or to enhance your foundational knowledge?

Statistics 1 Quiz

Regression Quiz

Regression Quiz

### Biostatistics

Entering the biostatistics field? Test your skill here.

Biostatistics Quiz

Statistics 2 Quiz

### Stay Informed

Our Blog

Read up on our latest blogs

Certificates

Courses

Find the right course for you