Exponential distribution is another most significant and extensively used continuous probability distribution. Exponential random variable is frequently used to model the time interval between two events. Exponential random variable is defined with a parameter ? and it’s represented as X~Exponential (?). In that sense the exponential random variable X defines the time interval between two consecutive events of a Poisson process with a mean of µ = ?. Here ? parameter defines the number of events is a certain time period. Therefore, it’s essential to use consistent time units in the determination of probabilities, mean and variance with the exponential random variable X. The mean (µ) and variance (?2) for exponential random variable X~Exponential (?) with parameter ? can be calculated from the following formulas,
E(x) = µ = 1/?
V (x) =?2 = 1/?2

Hence from above given formulas it’s clear that the mean and the standard deviation of the exponential distribution are equal.