ABSTRACT
In Chapter 2, the exponential distribution has been mentioned briefly. A random variable X is said to have the exponential distribution with scale parameter β if its pdf is given by
f(x ∣∣β) = 1
β e−x/β , x > 0 and β > 0 (6.1.1)
The mean of X or E(X) is β, and hence if X represents the life span of a randomly selected object in hours, then β stands for the mean life of all such objects having the exponential (6.1.1) life time distribution. One can use the reparameterization λ = 1/β and then the pdf (6.1.1) of X becomes
f(x ∣∣λ) = λe−λx, x > 0 and λ > 0 (6.1.2)
Note that with the pdf (6.1.2), E(X) = 1/λ, and λ = 1/E(X) is called the failure rate.
