Probability distribution function of a continuous random variable is a statistical measure that gives the probability that the random variable will take values in a given range. Generally the probability density is defined by the integral of the probability density function over a fixed interval. The total area under the pdf is 1.
Probability distribution functions can take various forms:
1. Uniform distribution: The simplest form of PDF in which all values in a given range [x0, x1] are equally likely.
i.e. P(X)= 1/(x1-x0) if x0 ≤ x ≤ x1
2. Normal Distribution Function: The most important PDF in which the probability density function is supposed to be Gaussian in nature. This is very closely related to the central limit theorem. The shape represents a bell shaped in which the function attains the peak in the central region (near the mean) and the tapers off towards the extremes
Probability density functions are very popular in the world of finance and used a lot in financial modelling to determine the behaviour of equity prices and other interest rates.