maths.free › Probability Theory › Random variables and expectation

Random variables and expectation

Distributions, expected value, variance, linearity of expectation.

A random variable is a number attached to each outcome; its expectation is the probability-weighted average, and expectation is linear even when the variables are dependent. Picture it: the distribution as a bar chart, the mean as its balance point. Think it: expectation is an integral against the probability measure.

Radni primjer · 10 * 1/2

Arithmetic · Arithmetic

Evaluate 10 * 1/2

\frac{10}{2}

Korak po korak

  1. 10 \cdot 1 \cdot \frac{1}{2} = 5

    Multiply: 10·1(1/2) = 5.

Otkrij odgovor
5

Now you Izaberite problem, ili tipkanje ili nacrtati vlastiti. Svaki korak, slika, odgovor skriven dok ne pitate.

Zadrži svoj rad

Besplatan račun dodaje bilješke na svakoj lekciji, zapis onoga što ste završili, rješeni problemi na jednom mjestu, i tutor možete pitati o ovoj stranici. Sama matematika je otvorena za sve, potpisani ili ne.

Prijavi se Prijava

Simboli koji se koriste ovdje

Dodirnite bilo koji simbol za punu definiciju, sliku, i što znači svako slovo u njoj.

Kako: Random variables and expectation

  1. Multiply: 10·1(1/2) = 5.

Pitanja koja ljudi postavljaju

What is the difference between probability and statistics?

Probability goes from a known model to what the data should look like; statistics goes from data back to the model. Probability theory is the deductive half.

What does the law of large numbers promise?

That the average of many independent samples converges to the expected value. It says nothing about any single trial.

Više u Probability Theory

Sample spaces and the axiomsThe common distributionsThe law of large numbers and the central limit theorem