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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.

Ýüklenen mysal · 10 * 1/2

Arithmetic · Arithmetic

Evaluate 10 * 1/2

\frac{10}{2}

Adım adım

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

    Multiply: 10·1(1/2) = 5.

Jawaby görkez
5

Indi sen Bir meseläni saýla, ýa-da ýaz ýa-da özüňi surata çek. Her ädim, bir resim, jogap sorag berlençä gizlenýär.

Özüň işle

Mugt hasap her bir ders üçin notlar goşýar, tamamlanan zadyňyzyň ýazgysyny, çözen problemaňyzy bir ýerde, we bu sahypa barada sorap biljek mugallymy. Matematika özüçe her kim üçin açyk, girseň ýa girmeseň.

_Gün _Giriş

Şu ýerde ulanylan simwollar

Eň täze düşündirme, surat, we her harpyň manysy üçin her bir simwoly basyň.

Nädip: Random variables and expectation

  1. Multiply: 10·1(1/2) = 5.

Adamlar soraýan soraglar

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.

_Ýaşa Probability Theory

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