# Difference between Probability density function and distribution function?

i am learning for my statistics exam and have to know a lot of theory. My question is:

Whats the difference between Probability density function and distribution function?

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The density (when it exists) is the derivative of the distribution function. –  Joel Cohen Jul 27 '12 at 13:31
Thx for your answer! Yes thats clear for me!!! But, where do you use it and especially why? –  Le Chifre Jul 27 '12 at 13:36
The relation between the probability density funtion $f$ and the cumulative distribution function $F$ is $$F(k) = \sum_{i \le k} f(i)$$ if $f$ is discrete and $$F(x) = \int_{y \le x} f(y)\,dy$$ if $f$ is continuous.
@maximus if the variable ranges over a discrete or continuous set of values. So if you're rolling a die, you have $\{1,2,3,4,5,6\}$, which is discrete. If you're picking a random point on a line, then your set is, say, the interval $[0,L]$ which is continuous. –  Robert Mastragostino Jul 27 '12 at 13:45