Probability density function

In probability and statistics, a probability density function is a function that characterizes any continuous probability distribution. For a random variable X, the probability density function of X is sometimes written as . The integral of the probability density function in the interval  yields the probability that a given random variable with the given density is contained in the interval provided. By definition, the probability density function is non-negative throughout its domain, on which the integral sums up to 1. 

 Probability density versus probability mass function 
The probability mass function is to a discrete probability distribution what the probability density function is to a continuous probability distribution. The probability density function is necessary to be able to work with continuous distributions. 

A random variable with a continuous probability distribution can take on any value within that distribution. Casting a dice will give the numbers 1 to 6, with a probability of , but this is not a continuous function, as only the numbers 1 to 6 are possible. 

In contrast, two people will not have the same height or the same weight. Using a probability density function, it is possible to determine the probability for people between  and , or between  and , even though there are infinitely many values between these two bounds.

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Category:Statistics