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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.

ຕົວຢ່າງ​ທີ່​ໄດ້​ເຮັດ · 10 * 1/2

Arithmetic · Arithmetic

Evaluate 10 * 1/2

\frac{10}{2}

ຂັ້ນ​ຕອນ​ຕໍ່​ຂັ້ນ​ຕອນ

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

    Multiply: 10·1(1/2) = 5.

ເປີດ​ເຜີຍ​ຄຳ​ຕອບ
5

ປັດຈຸບັນ​ທ່ານ ເລືອກ​ບັນຫາ ຫຼື ພິມ ຫຼື ແຕ້ມ​ເອງ. ທຸກ​ບາດກ້າວ, ຮູບ, ຄໍາຕອບ​ຖືກ​ລົບ​ຈົນ​ກວ່າ​ເຈົ້າ​ຈະ​ຖາມ​ມັນ.

ຮັກສາ​ການ​ເຮັດວຽກ​ຂອງ​ທ່ານ​ໄວ້

ບັນຊີຟຣີ ເພີ່ມ​ຂໍ້​ມູນ​ໃສ່​ບົດຮຽນ​ທຸກ​ບົດ, ບັນທຶກ​ຂອງ​ສິ່ງທີ່​ທ່ານ​ໄດ້​ເຮັດ​ແລ້ວ, ບັນຫາ​ທີ່​ທ່ານ​ໄດ້​ແກ້​ໄຂ​ໄວ້​ໃນ​ບ່ອນ​ດຽວ ແລະ ຄູ​ສອນ​ທີ່​ທ່ານ​ສາມາດ​ຖາມ​ກ່ຽວກັບ​ໜ້າ​ນີ້. ຄະນິດສາດ​ເອງ​ແມ່ນ​ເປີດ​ໃຫ້​ທຸກ​ຄົນ, ບໍ່​ວ່າ​ຈະ​ໄດ້​ເຂົ້າ​ສູ່​ລະບົບ ຫຼື ບໍ່.

ລົງທະບຽນ ចូល

ຕົວ​ສະ​ແດງ​ທີ່​ໃຊ້​ຢູ່​ທີ່​ນີ້

ກົດ​ຕົວ​ອັກສອນ​ໃດ​ໜຶ່ງ​ເພື່ອ​ເບິ່ງ​ຄວາມ​ໝາຍ​ເຕັມ, ຮູບ ແລະ ຕົວອັກສອນ​ແຕ່ລະ​ຕົວ​ໃນ​ມັນ​ໝາຍ​ຄວາມ​ວ່າ​ແນວໃດ.

ວິທີການ: Random variables and expectation

  1. Multiply: 10·1(1/2) = 5.

ຄໍາຖາມທີ່ຄົນຖາມ

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.

ເພີ່ມເຕີມໃນ Probability Theory

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