## Exponential Probabilities

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 . (1)

The cumulative distribution function (c.d.f.) is determined by integrating (1): . (2)
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 :

 1. , 2. , 3. .

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/ .