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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.

Eżempju maħdum · 10 * 1/2

Arithmetic · Arithmetic

Evaluate 10 * 1/2

\frac{10}{2}

Pass b'pass

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

    Multiply: 10·1(1/2) = 5.

Jiżvelaw it-tweġiba
5

Issa inti Agħżel problema, jew ittajpja jew iġbed tiegħek stess.Kull pass, stampa, it-tweġiba moħbija sakemm inti tistaqsi.

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Kont b'xejn iżid noti fuq kull lezzjoni, rekord ta' dak li lest, problemi solvuti tiegħek f'post wieħed, u għalliem inti tista' tistaqsi dwar din il-paġna.Il-matematika nnifisha hija miftuħa għal kulħadd, log fil jew le.

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Kif għandek tuża: Random variables and expectation

  1. Multiply: 10·1(1/2) = 5.

Mistoqsijiet li n-nies jistaqsu

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.

Aktar fil Probability Theory

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