What is Expectation values: Definition and 122 Discussions

In probability theory, the expected value of a random variable


{\displaystyle X}
, denoted



{\displaystyle \operatorname {E} (X)}



{\displaystyle \operatorname {E} [X]}
, is a generalization of the weighted average, and is intuitively the arithmetic mean of a large number of independent realizations of


{\displaystyle X}
. The expected value is also known as the expectation, mathematical expectation, mean, average, or first moment. Expected value is a key concept in economics, finance, and many other subjects.
By definition, the expected value of a constant random variable


{\displaystyle X=c}


{\displaystyle c}
. The expected value of a random variable


{\displaystyle X}
with equiprobable outcomes









{\displaystyle \{c_{1},\ldots ,c_{n}\}}
is defined as the arithmetic mean of the terms




{\displaystyle c_{i}.}
If some of the probabilities






{\displaystyle \Pr \,(X=c_{i})}
of an individual outcome



{\displaystyle c_{i}}
are unequal, then the expected value is defined to be the probability-weighted average of the



{\displaystyle c_{i}}
s, that is, the sum of the


{\displaystyle n}








{\displaystyle c_{i}\cdot \Pr \,(X=c_{i})}
. The expected value of a general random variable involves integration in the sense of Lebesgue.

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  1. LightPhoton

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  2. B

    Relation between Mutual information and Expectation Values

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  3. VVS2000

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  4. A

    Expectation Values <E> and <E^2>

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  5. astrocytosis

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  6. redtree

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  7. learn.steadfast

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  8. Technon

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  9. gasar8

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  10. thariya

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  11. C

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  12. RJLiberator

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  13. W

    Quantum Mechanics: Expectation values (Griffiths)

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  14. D

    I Factorising expectation values

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  15. G

    Expectation values as a phase space average of Wigner functions

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  16. B

    Expectation values and commutation relations

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  17. Leechie

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  18. M

    Wavefunction normalisation and expectation values

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  19. D

    Expectation values of the quantum harmonic oscillator

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  20. F

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  21. D

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  22. J

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  23. L

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  24. phys-student

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  25. edguy99

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  26. gfd43tg

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  27. Z

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  28. D

    Expectation Value of Operator A: c or Complex Conjugate?

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  29. T

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  30. Ryuzaki

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  31. R

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  32. S

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  33. carllacan

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  34. Ravi Mohan

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  35. H

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  36. X

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  37. D

    Probability of measuring E in a Hydrogen atom, and expectation values

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  38. C

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  39. D

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  40. Q

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  41. F

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  42. K

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  43. J

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  44. B

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  45. L

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  46. tomwilliam2

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  47. M

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  48. T

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  49. A

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  50. A

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