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.

ಕಾರ್ಯಗತಗೊಂಡ ಮಾದರಿ · 10 * 1/2

Arithmetic · Arithmetic

Evaluate 10 * 1/2

\frac{10}{2}

ಅಡಿಯಿಡು (step)

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

    Multiply: 10·1(1/2) = 5.

ಉತ್ತರವನ್ನು ತಿಳಿಸಿ
5

ಈಗ ನೀವು ಪ್ರತಿಯೊಂದು ಹೆಜ್ಜೆಯಲ್ಲಿ, ಒಂದು ಚಿತ್ರವನ್ನು ನೀವು ಕೇಳುವ ತನಕ ಅಡಗಿಸಿಟ್ಟಿಡಿರಿ.

ನಿಮ್ಮ ಸ್ವಂತ ಕೆಲಸವನ್ನು ಪೂರೈಸಿ

A free account adds notes on every lesson, a record of what you have finished, your solved problems in one place, and a tutor you can ask about this page. The maths itself is open to everyone, signed in or not.

ಮೇಲೆ ಗುರುತು ಹಾಕು ಪ್ರವೇಶ (ಲಾಗಿನ್)

ಇಲ್ಲಿ ಬಳಸಲಾದ ಸಂಕೇತಗಳು

ಈ ವಚನದಲ್ಲಿ ಬಳಸಲಾಗಿರುವ ಗ್ರೀಕ್‌ ಪದವು, ಚಿತ್ರ ಮತ್ತು ಚಿತ್ರಗಳನ್ನು ನೀವು ಸುಲಭವಾಗಿ ಅರ್ಥಮಾಡಿಕೊಳ್ಳಲು ಸಹಾಯ ಮಾಡುತ್ತದೆ.

ಹೇಗೆ: Random variables and expectation

  1. Multiply: 10·1(1/2) = 5.

ಜನರು ಕೇಳುವುದು

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.

ಇನ್ನಷ್ಟು Probability Theory

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