Discrete Probability Distribution Calculator
A discrete probability distribution calculator helps analyze random events with finite outcomes. It calculates key metrics like expected value, variance, and standard deviation, essential for probability analysis, risk assessment, and statistical modeling in fields like finance, engineering, and research.
Calculator
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
Derivation Process
The calculator uses probability axioms and discrete distribution properties. It first verifies valid probability inputs (sum=1), then computes weighted average for mean. Variance is calculated using squared deviations from mean, weighted by probabilities. Standard deviation is the square root of variance, providing spread measurement.
FAQs
What is a discrete probability distribution?
A discrete probability distribution describes probabilities of outcomes with distinct, separate values. It lists all possible values of a random variable with their corresponding probabilities, used in scenarios with countable outcomes like dice rolls or survey responses.
Why must probabilities sum to 1?
The total probability of all possible outcomes must equal 1 (100%) according to probability axioms. This ensures complete coverage of all possible events in the sample space.
Can I use fractions instead of decimals?
Yes, but the calculator requires decimal format. Convert fractions (e.g., 1/4 = 0.25) before inputting. The system automatically validates numerical inputs.