The applet in this section allows you see how probabilities are determined from the exponential distribution.
The exponential distribution is a continuous probability distribution and is quite often used to model rates of decay or growth or to model waiting times in a Poisson process.
The exponential distribution is completely specified by one parameter: the rate, .
The parameter must be strictly positive.
Due to limitations of screen size, the applet restricts to values between 0.2 and 5, inclusively.
For a random variable defined by, the probability density function (p.d.f.) is given by
The cumulative distribution function (c.d.f.) is determined by integrating (1):
Table 1 contains all the details for the exponential distribution.
Table 1. Details of the Exponential distribution.
The applet determines any of the three following probabilities from (2) for given :
Note: The Central Limit Theorem applet defines the exponential distribution using the parameter .
In that case is the mean of the exponential distribution rather than the rate, .
The two notations are equivalent by letting =1/.
See also: Probability Distributions, Normal Distribution, T Distribution.