Expected Value
Aligned to S-MD.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
This is a (+) advanced standard. The expected value of a random variable is the sum of each value times its probability: E(X) = Σ x × P(x). It is the long-run average, or mean, of the distribution.
Worked example
A game pays $1, $2, or $5 with probabilities 0.5, 0.3, and 0.2. Then E(X) = 1 × 0.5 + 2 × 0.3 + 5 × 0.2 = 0.5 + 0.6 + 1.0 = $2.10 per play on average.
Practice questions
- Write the formula for the expected value of a random variable.
- A die roll pays its face value in dollars. Find E(X).
- A raffle ticket wins $100 with probability 0.01 and $0 otherwise. Find its expected value.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Valor esperado
Este es un estándar avanzado (+). El valor esperado de una variable aleatoria es la suma de cada valor por su probabilidad: E(X) = Σ x × P(x). Es el promedio a largo plazo, o la media, de la distribución.
Ejemplo: Un juego paga $1, $2 o $5 con probabilidades 0.5, 0.3 y 0.2. Entonces E(X) = 1 × 0.5 + 2 × 0.3 + 5 × 0.2 = 0.5 + 0.6 + 1.0 = $2.10 por jugada en promedio.
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