Probability density function

2016-07-15T10:58:01Z

176.249.125.228: Fixed typo.

[[Image:Boxplot vs PDF.svg|thumb|350px|[[Boxplot]] and probability density function of a [[normal distribution]] {{nowrap|''N''(0, ''σ''<sup>2</sup>)}}.]]
A '''probability density function''' is a [[function (mathematics)|function]] that can be defined for any [[Continuous function|continuous]] [[probability distribution]]. The [[integral]] of the probability density function in the interval <math>[a,b]</math> yields the [[probability]] that a given [[random variable]] with the given density is contained in the interval provided.

The probability density function is necessary to be able to work with continuous distributions. Casting a [[dice]] will give the numbers 1 to 6, with a probability of <math>\tfrac 1 6</math>, 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 {{convert|180|cm}} and {{convert|181|cm}}, or between {{convert|80|kg|lb|1}} and {{convert|81|kg|lb|1}}, even though there are infinitely many values between these two bounds.

[[Category:Statistics]]

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Probability density function