A probability density function characterizes continuous random variables by assigning a probability density, rather than an exact probability, to possible values. Since the exact probability of any single continuous value is zero, determining the probability that the variable falls within a specific interval requires calculating the definite integral of the density function over that interval.

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The continuous probability distribution of the studentized range of an i.i.d. sample from a normally distributed population.
Differentiating the cumulative distribution function with respect to q gives the probability density function.

Studentized Range Distribution

A continuous random variable can take on any value at any point along a given interval. This variable is a real number. Continuous data is measured.

Continuous Random Variable

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

An Introduction to Statistical Learning with Applications in R

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Probability Density Function

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