# Exponential Distribution Calculator

## Exponential Distribution

Welcome to our comprehensive resource for exponential distribution calculations. Our robust Exponential Distribution Calculator is designed to provide accurate results quickly and efficiently.

## What is Exponential Distribution?

Exponential distribution is a vital statistical concept typically used for modeling time intervals in a Poisson process, a sequence of events that occur randomly and independently at a given average rate.

Defined by the parameter λ (lambda), the average rate of events per time interval, the exponential distribution's probability density function (PDF) and cumulative distribution function (CDF) are as follows:

**PDF:**f(x;λ) = λe^{-λx} \quad \text{for} \quad x \geq 0, λ > 0**CDF:**F(x;λ) = 1 - e^{-λx} \quad \text{for} \quad x \geq 0

## The Magic of Our Exponential Distribution Calculator

Our calculator is a state-of-the-art tool that utilizes these mathematical formulas to perform complex calculations instantly. It's simple and easy to use. Here's a step-by-step guide on how to utilize it:

**Enter the Lambda (λ) Value:**This is the average rate of events occurring per unit of time.**Specify the 'X' Value:**This is the specific time point for which you want to calculate the probability.**Get Result:**After entering the necessary details, you will get the result instantaneously.

## Practical Example

Let's illustrate how the calculator works with a practical example. Suppose you wish to compute the PDF and CDF of an exponential distribution for a rate (λ) of 0.5 and at a time point (x) of 2.

- Enter the λ value as 0.5
- specify 'X' value as 2
- The result, will appear instantly.

For PDF:0.5 * e^{-0.5*2} = 0.18394For CDF:1 - e^{-0.5*2} = 0.63212

By using our calculator, you can avoid complex manual computations, ensuring precise results in an instant.

Our tool serves as more than just a calculator. It's a platform designed to facilitate learning and understanding of exponential distribution in a practical and efficient manner. It takes away the complexity of manual computations and introduces you to a straightforward and efficient way of dealing with statistical distributions.

- Probability and Discrete Distributions
- Continuous Distributions and Data Visualization