Estimate PMF and CDF across key discrete models. Compare outcomes, review steps, and export results for clear probability decision work.
| x | PMF | CDF |
|---|---|---|
| 0 | 0.11718750 | 0.11718750 |
| 1 | 0.23437500 | 0.35156250 |
| 2 | 0.23437500 | 0.58593750 |
| 3 | 0.15625000 | 0.74218750 |
PMF gives the probability of one exact discrete outcome. It answers the chance that the random variable equals a chosen value.
CDF gives the cumulative probability up to that value. It answers the chance that the random variable is less than or equal to a chosen value.
For binomial models, use combinations with success probability. For Poisson models, use the rate parameter. For geometric models, count trials until the first success. For discrete uniform models, each allowed value has the same probability.
Select a probability model first. Enter the needed parameters for that model. Then enter the target x value. Press the calculate button to generate PMF, CDF, mean, variance, and a probability table. Use the CSV button to save tabular output. Use the PDF button to print or save the page.
PMF and CDF are core tools in statistics. They help describe discrete random variables. A PMF gives the chance of one exact outcome. A CDF gives the total chance up to a selected value. Together, they support clear probability analysis.
The probability mass function focuses on one point. If you want the chance of exactly three successes, the PMF gives that answer. This is useful in quality checks, risk studies, and experiment planning. It is precise and easy to interpret.
The cumulative distribution function adds probabilities from the lowest value up to x. This makes it useful for threshold questions. You can test whether an event stays below a limit. Many business and research decisions use cumulative probabilities.
Binomial models work with repeated trials. Poisson models fit event counts in fixed intervals. Geometric models track the first success. Discrete uniform models assume equal likelihood across allowed values. Each model serves a different type of real problem.
This calculator combines several models in one place. It returns PMF, CDF, mean, and variance. It also builds a table for fast checking. That saves time during homework, reporting, and practical analysis tasks.
Always match the distribution to the data structure. Check whether outcomes are discrete. Review parameter limits before calculating. Then compare the exact probability with the cumulative probability. This approach reduces mistakes and improves interpretation.
PMF gives the probability of one exact discrete value. CDF gives the probability that the value is less than or equal to a chosen point.
Use it when you have a fixed number of trials, only two outcomes per trial, and the same success probability in each trial.
Use Poisson for counting events in a fixed time, area, or space when events occur independently and the average rate stays stable.
It measures the probability that the first success happens on a specific trial. It also provides the cumulative chance up to a trial number.
No. This tool is built for discrete probability models only. Continuous models use density functions instead of probability mass functions.
That happens when x is outside the allowed support or when model parameters are invalid for the selected distribution.
CDF is a cumulative probability. All probabilities must stay within the full probability scale from zero to one.
Mean shows the expected center of the distribution. Variance shows spread. They help you understand location and dispersion, not just one probability.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.