Probability Distribution Calculator
A probability distribution calculator helps determine likelihood outcomes in statistical experiments. It calculates key metrics like mean, variance, and standard deviation, essential for predicting patterns in data analysis, quality control, and risk assessment across various fields including finance and research.
Formula
Mean (μ) = Σ(xi * pi)
Variance (σ²) = Σ[(xi - μ)² * pi]
Standard Deviation (σ) = √σ²
How to Use
1. Enter numeric outcomes separated by commas
2. Enter corresponding probabilities (sum must be 1)
3. Click Calculate
4. Results show mean, variance, and standard deviation
5. Use Clear button to reset
FAQs
What is a probability distribution calculator?
A probability distribution calculator is a tool that computes key statistical measures (mean, variance, standard deviation) from given outcomes and their probabilities, helping analyze random variable behavior in statistical experiments.
Why is probability distribution important?
Probability distributions help predict outcomes in uncertain situations. They're fundamental in statistics for modeling real-world phenomena, risk assessment, and decision-making processes across finance, engineering, and scientific research.
Can I use fractions instead of decimals?
Yes, but the calculator requires decimal inputs. Convert fractions to decimals (e.g., 1/4 = 0.25) and ensure the total probability sums to exactly 1.
What if probabilities don't sum to 1?
The calculator will show an error. Valid probability distributions must have probabilities that sum exactly to 1. Adjust values accordingly.
Which distributions can this calculator handle?
This handles discrete probability distributions. For continuous distributions (like normal distribution), different calculators using integration are required.
How accurate are the results?
Results are precise to 4 decimal places. Accuracy depends on correct input values and proper probability distribution validation.
Can I calculate binomial probabilities?
This calculator handles custom distributions. For binomial specifically, you'd need to input all possible outcomes and their binomial probabilities manually.
What's the difference between variance and standard deviation?
Variance measures spread squared, while standard deviation is the square root of variance, providing comparable units to the mean. Both measure distribution dispersion.
Can I save my calculations?
This version doesn't save data. Copy results manually. Future versions might include save/export features.
Is this calculator mobile-friendly?
Yes, the responsive design works on all devices. Input fields and results adjust automatically to screen size for optimal usability.