1. What Is Exponential Distribution?

The exponential distribution describes the time between events in a Poisson process, where events occur continuously and independently at a constant average rate. It's a continuous probability distribution often used to model waiting times.

2. How To Calculate Rate Parameter

The rate parameter (λ) is calculated as:

Where:

• \( \lambda \) — Rate parameter (events per time unit)
• Mean — Average time between events

Explanation: The rate parameter is the reciprocal of the mean time between events. A higher λ means events occur more frequently.

3. Applications of Exponential Distribution

Details: Used in reliability engineering (time to failure), queuing theory (service times), and telecommunications (time between phone calls). It's memoryless, meaning the probability of an event occurring is independent of how much time has already elapsed.

4. Using the Calculator

Tips: Enter the mean time between events in any consistent time units (seconds, hours, days, etc.). The result will be in reciprocal time units (events per time unit).

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between exponential and Poisson distributions?
A: Poisson describes number of events in fixed interval, while exponential describes time between events. They share the same λ parameter.

Q2: What are typical units for λ?
A: Units are reciprocal of your time units (e.g., if mean is in hours, λ is in events/hour).

Q3: What does the memoryless property mean?
A: The probability an event occurs in the next time interval doesn't depend on how much time has already passed.

Q4: When is exponential distribution not appropriate?
A: When event rates vary over time or events aren't independent (e.g., earthquake occurrences).

Q5: How is this related to the geometric distribution?
A: Exponential is continuous version of discrete geometric distribution.