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Exponential Distribution Calculator

Statistics
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Calculates probabilities related to the time until an event occurs in a Poisson process. The exponential distribution models the time until an event happens, given an average rate of occurrence.

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How To Use

How to use this calculator

Start with your values, or try a preset.

Step 1

Enter Rate Parameter (位) and Time (t) in the units shown.

Step 2

Read Median Time, Mean (Average Time), Cumulative Distribution Function (CDF), and Probability Density Function (PDF) in the results panel. Results update as you change the inputs.

Step 3

Choose a preset to load an example, then adjust the values for your situation.

Worked Examples

Example calculations

See the inputs and their calculated results.

位 = 1, t = 1

Rate Parameter (位): 1; Time (t): 1

Median Time: 0.6931471806; Mean (Average Time): 1; Cumulative Distribution Function (CDF): 0.6321205588; Probability Density Function (PDF): 0.3678794412

位 = 2, t = 0.5

Rate Parameter (位): 2; Time (t): 0.5

Median Time: 0.3465735903; Mean (Average Time): 0.5; Cumulative Distribution Function (CDF): 0.6321205588; Probability Density Function (PDF): 0.7357588823

位 = 0.5, t = 2

Rate Parameter (位): 0.5; Time (t): 2

Median Time: 1.386294361; Mean (Average Time): 2; Cumulative Distribution Function (CDF): 0.6321205588; Probability Density Function (PDF): 0.1839397206

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