Probability density function

A probablity density function is a function that can be defined for any continous probability distribution. The integral of the porbabiliy 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 {{convert|80|kg]] and 81 kilograms (179 lb), even thought there are infinitely many values between these two bounds.