Exponential Distribution Calculator

How to Use the Exponential Distribution Calculator

The Exponential Distribution Calculator is designed to help you compute various statistical properties of an exponential distribution given a rate parameter (λ) and x value. Follow the steps below to use the calculator effectively.

Step 1: Enter the Rate Parameter (λ)

Rate Parameter (λ): The first input you need to provide is the rate parameter, denoted by λ.

Instructions:

• Locate the input field labeled Rate Parameter (λ).
• Enter a positive numerical value for λ, which represents the rate of events occurring. Ensure that λ is greater than 0.
• The input field will only accept numbers with a minimum value of 0.0001, and you can increment or decrement by 0.0001.

Step 2: Provide the X Value

X Value: The second input required is the x value, which typically represents the time or space over which the exponential distribution is evaluated.

Instructions:

• Locate the input field labeled X Value.
• Enter a numerical value for x. Ensure that x is a non-negative number (x ≥ 0).
• The input field accepts numbers in increments of 0.0001.

Step 3: View the Results

Once you have entered both the rate parameter and x value, the calculator will compute several properties of the exponential distribution. Below is a list of results you will receive:

• Probability Density f(x): Calculated using the formula: λ * exp(-λ * x). This represents the value of the probability density function at x.
• Cumulative Probability F(x): Calculated as 1 – exp(-λ * x). This represents the cumulative probability up to x.
• Mean (Expected Value): Given by 1 / λ, it represents the average expected value of the distribution.
• Variance: Calculated as 1 / (λ * λ), it indicates the variance of the distribution.
• Standard Deviation: This is simply 1 / λ, representing the standard deviation of the distribution, equivalent to the mean for the exponential distribution.
• Median: Derived as ln(2) / λ, it represents the median of the distribution.

Results are formatted to ensure precision and readability: Probability Density and Cumulative Probability are displayed with six decimal places, while Mean, Variance, Standard Deviation, and Median are displayed with four decimal places.