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(X_{1} < X < X_{2}) = e^{-cX1} - e^{-cX2}

Mean: μ = 1/c

Median: m = (LN(2))/c. (LN means Natural log)

Standard Deviation: σ = 1/c

Variance: σ^{2} = 1/c^{2}

Note: Value C must be Positive.

**Exponential Distribution Solved Example:**

Calculate the Exponential Distribution whose C is 5, X_{1} = 1, X_{2} = 2

Substitute these values in the above formulas,

P(X_{1} < X < X_{2}) = 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**

σ^{2} = 1/c^{2}

= 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.

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