Probability density function

Boxplot and probability density function of a normal distribution N(0, σ²).

A probablity density function is a function that can be defined for any continous probability distribution. The integral of the probabiliy density function in the interval $[a,b]$ yields the probability that a given random variable with the given density is contained in the interval provided.

The probabliity density function is necessary to be able to work with continous distributions. Casting a dice will give the numbers 1 to 6, with a probability of ${\tfrac {1}{6}}$, 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 probabiliy for people between 180 centimetres (71 in) and 181 centimetres (71 in), or between 80 kilograms (176.4 lb) and 81 kilograms (178.6 lb), even thought there are infinitely many values between these two bounds.