The probability density function, often denoted as pdf, is a function that describes the probability of finding a random variable within a defined range. The significance of the pdf, f(x), is that f(x)dx is the probability that the random variable x' is in the interval (x, x + dx). This is often written as P(x x' x + dx) = f(x)dx. Since f(x)dx is a probability it is unitless and therefore f(x) has the units of inverse random variable units. It is also possible to define the probability of finding the random variable somewhere in a finite interval. P(a x b) = ^b_a f(x)dx, where the finite interval is [a, b]. This probability is equal to the area under the curve defined by f(x) from a to b.

As with other probability distributions the...