Compute the expected value E[X] from a discrete probability distribution table.
The expected value E[X] is the long-run average of a random variable. For a discrete distribution, it is the probability-weighted sum of all possible values: E[X] = Σ xᵢ × P(xᵢ).
Expected Value
E[X] = Σ xᵢ × P(xᵢ)
Variance
Var(X) = Σ P(xᵢ) × (xᵢ − E[X])²
No. For example, the expected value of a fair die roll is 3.5, which is not a possible outcome. It represents the long-run average.
For a probability distribution, the expected value IS the mean (μ). For sample data, the sample mean estimates the population expected value.