Course Content
Probability Theory Basics
4. Commonly Used Continuous Distributions
5. Covariance and Correlation
Probability Theory Basics
Exponential Distribution
The exponential distribution is a continuous probability distribution that models the time between events in a Poisson process.

We remember that the Poisson process describes the number of events that occurred during some period of time. On the other hand, exponential distribution describes the time between the occurrence of two successive events (the distance between two adjacent non-zero points in the graph above).
Poisson distribution is parameterized by mu
parameter, which describes the average number of accidents by the time unit. The exponential distribution is parametrized by the parameter scale
which determines the average time between two accidents.
Note
There is a clear relationship between the Poisson process parameter
mu
and the exponential distribution parameterscale
:mu
=1 \ scale
for one unit of time
Let's look at the example.
Suppose the average time between customer arrivals at a store is 5
minutes. What is the probability that the next customer arrives within 3
minutes?
We have a Poisson process where an event is the customer's arrival. The average time between two arrivals is 5
minutes. As a result, we can use exponential distribution to calculate the corresponding probability:
We also use .cdf()
method of the scipy.stats.expon
class with a specified scale
parameter to calculate the corresponding probability on the interval [0,3]
.
The exponential distribution can be used to model:
Select the correct answer
Everything was clear?