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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.

Kugwira ntchito chitsanzo · 10 * 1/2

Arithmetic · Arithmetic

Evaluate 10 * 1/2

\frac{10}{2}

Gawo ndi Gawo

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

    Multiply: 10·1(1/2) = 5.

Kusonyeza yankho
5

Tsopano inu Sankhani vuto, kapena kulemba kapena kujambula wanu. Pakalipano, yankho limeneli lidzapezeka patsamba lino.

Kusunga ntchito yanu yokha

M’malo mwake, maakaunti aulere amawonjezera malemba pazophunzira zonse, mnda wa zomwe mwamaliza, mavuto anu omaliza m’malo limodzi, ndi m’bale amene mungafunse za nkhaniyo. Maphunziro a matekinoloje ndi otsegulira kwa aliyense, olembetsa kapena osalembetsa.

Kulembetsa Kulowa

Zithunzi

Pitani pa dzina lililonse lachifaniziro kuti mudziwe tanthauzo lake, chithunzi chake, ndi zimene limatanthauza.

Momwe mungagwiritsire ntchito: Random variables and expectation

  1. Multiply: 10·1(1/2) = 5.

Mafunso omwe anthu amafunsa

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.

Zambiri pa Probability Theory

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