Probability Density Function
The density of a differentiable distribution function ; probabilities integrate it.
Definition 4.3 (Probability Density Function)
Let be a continuous random variable with probability distribution function . If is differentiable, then the probability density function of is defined as
Properties
If has probability density function , then:
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for all ;
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;
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for all , and more generally for every .
If is discrete, , so the integral formula is the continuous analogue of the discrete sum. For small ,
so is proportional to the probability that takes values around .
Related
Stated in
- Definition 4.3 (Probability Density Function)§4.1 Probability Distribution Function