Exponential Distribution Formula, Example

The exponential distribution is a simple distribution also commonly used in reliability engineering. The formula used to calculate Exponential Distribution Calculation is,
Exponential Distribution Formula:
P(X₁ < X < X₂) = e^-cX₁ - e^-cX₂
Mean: μ = 1/c
Median: m = (LN(2))/c. (LN means Natural log)
Standard Deviation: σ = 1/c
Variance: σ² = 1/c²
Note: Value C must be Positive.

Exponential Distribution Solved Example:
Calculate the Exponential Distribution whose C is 5, X₁ = 1, X₂ = 2
Substitute these values in the above formulas,
P(X₁ < X < X₂) = e^-cX₁ - e^-cX₂
P(1 < X < 2) = e^-(5x₁) - e^-(5x₂)
= e^-(5) - e^-(10) (e Power x Calculator)
= 0.0067 - 0
= 0.0067

Mean
μ = 1/c
= 1/5
= 0.2

Median
m = (LN(2))/c. (LN means Natural log)
Natural log of 2 is 0.6932. Calculate Log value using Log Calculator
m = 0.6932/5
= 0.13864

Standard Deviation
σ = 1/c
= 1/5
= 0.2

Variance
σ² = 1/c²
= 1/52
= 0.04

The above worksheet is an walk through to understand the concept of Exponential Distribution and the example problem shows how to calculate the Exponential distribution for the given data. When try such calculations on your own, use this exponential distribution calculator to verify your results.