Random Variables and Probability Distributions
Aligned to S-MD.A.1 — Common Core State Standards for Mathematics.
What this lesson teaches
This is a (+) advanced standard. A random variable assigns a number to each outcome of a chance process. Its probability distribution lists each value with its probability; all probabilities are between 0 and 1 and together sum to 1.
Worked example
Let X be the number of heads in two coin flips. The outcomes give TT → 0, HT and TH → 1, and HH → 2, so the distribution is P(0) = 1/4, P(1) = 1/2, P(2) = 1/4. These probabilities sum to 1.
Practice questions
- Define a random variable for the roll of one die.
- For two coin flips, what is P(X = 1) where X is the number of heads?
- The probabilities in any distribution must sum to what 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
Variables aleatorias y distribuciones de probabilidad
Este es un estándar avanzado (+). Una variable aleatoria asigna un número a cada resultado de un proceso al azar. Su distribución de probabilidad enumera cada valor con su probabilidad; todas las probabilidades están entre 0 y 1 y juntas suman 1.
Ejemplo: Sea X el número de caras en dos lanzamientos de moneda. Los resultados dan TT → 0, CX y XC → 1, y CC → 2, así que la distribución es P(0) = 1/4, P(1) = 1/2, P(2) = 1/4. Estas probabilidades suman 1.
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