Exponential distribution

Definition

Exponential distribution is a continuous probability distribution used to model the time between events in a Poisson process. It is characterized by its constant hazard rate, meaning the event rate is consistent over time.

5 Must Know Facts For Your Next Test

1. The exponential distribution is defined by a single parameter, lambda (λ), which is the rate parameter.
2. It has a memoryless property, meaning the probability of an event occurring in the future is independent of how much time has already elapsed.
3. The mean and standard deviation of an exponential distribution are both equal to 1/λ.
4. It is commonly used to model waiting times or lifetimes of certain financial instruments or systems.
5. The probability density function (PDF) for an exponential distribution is given by f(x;λ) = λe^(-λx) for x ≥ 0.

Review Questions

• What does the parameter lambda (λ) represent in an exponential distribution?
• How does the memoryless property affect the interpretation of an exponential distribution?
• What are the mean and standard deviation of an exponential distribution with a rate parameter λ?

Related terms

Poisson Process: A statistical process that models random events occurring independently over time at a constant average rate.

Probability Density Function (PDF): A function that describes the likelihood of a random variable taking on a particular value in a continuous probability distribution.

Hazard Rate: The rate at which events occur over time, often used in survival analysis and reliability engineering.