Example: waiting-time density at twelve minutes
Assume exponentially distributed waits with a mean of twelve minutes. Evaluate the density at twelve minutes.
Download the scenario reference (CSV)This is the same example used in Help. The CSV lists reference scenarios. Enter the selected scenario manually on Inputs; importing it does not configure this calculator. Use Open example in a practice copy in Help to prefill the inputs.
1. Create the workspace
In the sidebar, open Basic Statistics and choose Distributions. Create an analysis, name it, select New blank worksheet, then choose Create analysis.
2. Choose the calculation
On Inputs, choose Continuous for Distribution type, Exponential for Distribution, then Probability density (PDF) for Calculation.
3. Enter the model
Choose Mean θ for Exponential parameter. Enter 12 in Mean (θ), in minutes.
4. Enter the question
Choose Single value for Value source. Enter 12 in Value (x), in minutes. No worksheet columns are assigned.
5. Run analysis
Choose Run analysis, then open Results.
6. Interpret results
Check the question
Assume exponentially distributed waits with a mean of twelve minutes. Evaluate the density at twelve minutes.
Read the calculated value
The PDF is 0.0306566 per minute. It is the height of the density curve at twelve minutes.
Understand what it means
Density is not a probability. An exact point has probability zero in this continuous model. The probability of a time interval is an area under the curve.
Use the model carefully
For a practical question, define an interval, such as ten to fifteen minutes. Subtract the CDF at ten from the CDF at fifteen to find its modeled probability.
More details: read each result section
Complete result tables use six significant digits, as in Help.
Distribution values
x is the entered time in minutes. PDF is the density at x, with units of inverse minutes. Do not convert it directly to a percent probability. Density is not a probability. An exact point has probability zero in this continuous model. The probability of a time interval is an area under the curve.
| x | |
|---|---|
| 12 | 0.0306566 |
Distribution summary
Type distinguishes continuous values from whole-number counts. Distribution names the model. Calculation records PMF (exact-count probability), PDF (density), CDF (cumulative probability) or ICDF (quantile). The remaining rows record the active parameters; they are assumptions entered on Inputs.
| Setting | Value |
|---|---|
| Type | Continuous |
| Distribution | Exponential |
| Calculation | |
| Mean (θ) | 12 |
- Exponential(mean θ=12.0) via expon(scale=θ)
7. Create a report
Keep Distribution values (or the quantile table) and Distribution summary. State the model assumptions, time unit or count interval, and the question being answered. Density is not a probability. An exact point has probability zero in this continuous model. The probability of a time interval is an area under the curve.
Choose Add to report from the completed run. Open Choose individual items and advanced options to select tables and charts, then choose Add to draft. Hidden items stay in the saved analysis.
Name the report and add the purpose of the study and your interpretation. Choose Save, review Preview, then use Export → Download HTML. The example below contains the full selected content, including results beyond one screen.