The exponential distribution is a continuous probability distribution that describes the time between events in a Poisson process, where events occur at a constant rate and independently of each other. The mean and variance of the exponential distribution are related as follows:
The mean of an exponential distribution is equal to the inverse of the rate parameter (λ): mean = 1/λ.
The variance of an exponential distribution is equal to the square of the inverse of the rate parameter: variance = 1/λ^2.
In other words, the variance of an exponential distribution is proportional to the square of its mean. This relationship between the mean and variance of the exponential distribution is important in many statistical applications, such as modeling the time between failures in a system or the inter-arrival times of customers in a queue.