Probability Distribution Calculator
Find the mean, variance and standard deviation of a discrete probability distribution from its values and probabilities.
Change the values and press Calculate to work out your own figures.
Enter the values and their probabilities, in the same order.
| x | P(x) | x × P(x) |
|---|---|---|
| 0 | 0.1 | 0 |
| 1 | 0.3 | 0.3 |
| 2 | 0.4 | 0.8 |
| 3 | 0.2 | 0.6 |
Show the working
- E(X) = Σ x × P(x) = 0 × 0.1 + 1 × 0.3 + 2 × 0.4 + 3 × 0.2 = 1.7
- Var(X) = Σ (x − μ)² P(x) = 0.81
How to use it
Enter the values and their probabilities, in the same order.
Probabilities can be typed as decimals, fractions or percentages. Show the working gives the formula with your numbers in it.
Key facts
μ = Σ x P(x); σ² = Σ (x − μ)² P(x)
Discrete distributions
A discrete distribution lists every possible value and its probability; the probabilities must add up to 1.
Questions
What is the mean of a distribution?
Σ x P(x), the expected value.
How is the variance found?
Σ (x − μ)² P(x).
Formulas
μ = Σ x P(x); σ² = Σ (x − μ)² P(x)
Sources
Limitations
- Probabilities can be typed as decimals (0.25), fractions (1/4) or percentages (25%).