0Exponential Distribution:
Let’s consider the call center example one more time. What about the interval of time between the calls ? Here, exponential distribution comes to our rescue. Exponential distribution models the interval of time between the calls.
Other examples are:
1. Length of time beteeen metro arrivals,
2. Length of time between arrivals at a gas station
3. The life of an Air Conditioner
Exponential distribution is widely used for survival analysis. From the expected life of a machine to the expected life of a human, exponential distribution successfully delivers the result.
A random variable X is said to have an exponential distribution with PDF:
f(x) = { λe-λx, x ≥ 0
and parameter λ>0 which is also called the rate.
For survival analysis, λ is called the failure rate of a device at any time t, given that it has survived up to t.
Mean and Variance of a random variable X following an exponential distribution:
Mean -> E(X) = 1/λ
Variance -> Var(X) = (1/λ)².
