What is Probability density function?
[[Image:Boxplot vs PDF.svg|thumb|350px|[[Boxplot]] and probability density function of a [[normal distribution]] {{nowrap|''N''(0,&thinsp;''σ''<sup>2</sup>)}}.]] In [[probability]] and [[statistics]], a '''probability density function''' is a [[function (mathematics)|function]] that characterizes any [[Continuous function|continuous]] [[probability distribution]]. For a [[random variable]] ''X'', the probability density function of X is sometimes written as <math>f_X(x)</math>.<ref>{{Cite web|date=2020-04-26|title=List of Probability and Statistics Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/probability-statistics-symbols/|access-date=2020-09-13|website=Math Vault|language=en-US}}</ref> 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.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Probability Density Function|url=https://mathworld.wolfram.com/ProbabilityDensityFunction.html|access-date=2020-09-13|website=mathworld.wolfram.com|language=en}}</ref> By definition, the probability density function is non-negative throughout its domain, on which the integral sums up to 1.<ref>{{Cite web|last=Nykamp|first=Duane|date=|title=The idea of a probability density function|url=https://mathinsight.org/probability_density_function_idea|archive-url=|archive-date=|access-date=September 13, 2020|website=Math Insight}}</ref> == Probability density versus probability mass function == The [[probability mass function]] is to a [[Discrete mathematics|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 <math>	frac 1 6<