Could anyone explain to me that why:let u=E[X]. then

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Discussion Overview

The discussion revolves around the concept of expectation in probability theory, specifically questioning the relationship between a random variable and its expected value. Participants explore the implications of defining a variable as the expectation of another variable.

Discussion Character

  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant asks why, if u is defined as E[X], the expectation E[u] equals E[X].
  • Another participant asserts that since u is defined as E[X], its expectation value must also be E[X].
  • A different participant introduces a condition stating that if X is almost everywhere equal to a constant a, then E[X] equals that constant, suggesting a need for clarity on the definition of expectation.
  • A repeated query emphasizes confusion regarding the relationship between u and E[X], reiterating the question posed initially.
  • It is noted that if a random variable is constant, its average is that constant, which may relate to the earlier points about expectation.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and clarity regarding the relationship between a random variable and its expectation, with some asserting that the expectation of a defined constant is straightforward, while others seek further clarification on definitions and conditions.

Contextual Notes

The discussion highlights potential variations in the definition of expectation, which may affect the understanding of the claims made. There is also an implicit assumption regarding the nature of the random variable X that is not fully explored.

rukawakaede
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could anyone explain to me that why:

let u=E[X]. then E=E[X]?

I am a bit confused. Thanks.
 
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'u' is defined to be E[X]. It always going to be E[X]. Thus its expectation value is E[X].
 


In general, if X=a a.e., then E[X]=a. If you want me to prove this, then you first need to tell me how you defined expectation, since the definition tends to vary...
 


rukawakaede said:
could anyone explain to me that why:

let u=E[X]. then E=E[X]?

I am a bit confused. Thanks.


If a random variable is constant, then its average is that constant.
 

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