Random Variable Characteristics Calculator
Calculate Expectation (Mean), Variance, and Standard Deviation for discrete random variables. Validates probability distribution sums.
| Value (x) | Probability (p) | Action |
|---|---|---|
About
In probability theory, a discrete random variable is defined by a list of specific values and their associated probabilities. Students often need to derive the central tendency and dispersion of these datasets. This tool calculates the Expectation (weighted average), Variance (spread), and Standard Deviation. It strictly enforces the axiom that the sum of all probabilities in a valid distribution must equal 1. The calculation breakdown assists in verifying manual homework steps.
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probability distribution
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Formulas
Expectation (Mean):
μ = n∑i=1 xi ⋅ pi
Variance:
σ2 = ∑ (xi2 ⋅ pi) − μ2
Reference Data
| Metric | Symbol | Formula | Concept |
|---|---|---|---|
| Expectation | E[X] | ∑ x ⋅ p | The long-run average value. |
| Variance | Var(X) | E[X2] − (E[X])2 | Measure of spread squared. |
| Std Deviation | σ | √Var | Spread in original units. |
Frequently Asked Questions
The sum of probabilities for all possible outcomes in a sample space must equal 1 (or 100%) because it is certain that one of the outcomes will occur. If the sum is not 1, the distribution is not valid.
This calculator is for Discrete variables which take on distinct, countable values (e.g., number of heads in coin flips). Continuous variables can take any value within a range and require integrals rather than sums for calculation.