Calculator
Enter discrete outcomes and matching probabilities. The probabilities must add up to 1.
Plotly Probability Graph
Example Data Table
This sample shows a simple discrete distribution.
| Outcome (x) | Probability P(x) | x × P(x) |
|---|---|---|
| 1 | 0.10 | 0.10 |
| 2 | 0.15 | 0.30 |
| 3 | 0.20 | 0.60 |
| 4 | 0.25 | 1.00 |
| 5 | 0.20 | 1.00 |
| 6 | 0.10 | 0.60 |
| Total | 1.00 | 3.60 |
The mean expected value in this example is 3.60.
Formula Used
The expected value of a discrete random variable is:
E(X) = Σ [x × P(x)]
Here, x is an outcome value. P(x) is its probability. Multiply each outcome by its probability. Then add all products.
Extra Measures
Variance = Σ [(x - E(X))² × P(x)]
Standard Deviation = √Variance
These help you understand spread around the expected value.
How to Use This Calculator
- Enter each possible outcome in the outcome fields.
- Enter the matching probability for each outcome.
- Make sure all probabilities add up to exactly 1.
- Click the calculate button.
- Review the expected value, variance, and deviation.
- Use CSV or PDF export when needed.
- Check the graph for probability distribution shape.
Frequently Asked Questions
1. What is mean expected value?
Mean expected value is the weighted average of all possible outcomes. Each value is multiplied by its probability. Then the products are added together.
2. When should I use this calculator?
Use it when outcomes have known probabilities. It helps in probability, games, finance, forecasting, and risk analysis.
3. Do probabilities need to total one?
Yes. A valid discrete probability distribution must total 1. The calculator checks that rule before showing results.
4. Can expected value be negative?
Yes. If negative outcomes have enough weight, the expected value can be below zero.
5. What does variance show here?
Variance measures how spread out the outcomes are around the expected value. Larger variance means greater dispersion.
6. Why is standard deviation useful?
Standard deviation gives spread in the same units as the outcomes. That makes interpretation easier than variance alone.
7. What type of data fits this tool?
This tool fits discrete outcomes with assigned probabilities. Continuous distributions need integration, not simple row addition.
8. Does the graph change after calculation?
Yes. The graph updates using your submitted values. It plots outcomes on the x-axis and probabilities on the y-axis.
Printable Summary
This section appears during printing and PDF saving.