Does the Limit of Sample Expectations Equal the Limit of x_m?

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Discussion Overview

The discussion revolves around the relationship between the limit of sample expectations and the limit of a sequence denoted as x_m. Participants explore whether the limit of the expectation of samples converges to the same value as the limit of x_m, with a focus on proving this relationship.

Discussion Character

  • Homework-related, Exploratory, Technical explanation

Main Points Raised

  • One participant proposes that if lim x_m = n, then lim (expectation of samples x_i) should also equal n.
  • Another participant emphasizes the forum's guidelines regarding homework help, suggesting that complete solutions should not be provided without prior effort from the questioner.
  • A later reply indicates that the original poster found a solution independently, using the definition of limit and applying an inequality.

Areas of Agreement / Disagreement

There is no consensus on the proof itself, as the initial claim remains unproven within the discussion. Participants express differing views on how to approach the problem, and the guidelines for providing assistance in homework contexts are also highlighted.

Contextual Notes

Limitations include the lack of detailed mathematical steps in the initial claim and the absence of a formal proof within the discussion. The reliance on definitions and inequalities is mentioned but not fully explored.

Jekertee
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Given lim x_m=n
Prove that lim (expectation of samples x_i [with i=[1,m]]) = n too
:blushing: Thank you
 
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EDIT: Solution removed
 
Last edited:
Welcome to PF, Token.

I gather that you might not be familiar with the guidelines of the forum, especially for homework help. Please don't post complete solutions for homework problems.

https://www.physicsforums.com/showthread.php?t=5374
On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.
 
:redface: Thanks for the try, Token, if you has made more posts on PF,
I am not sure if there were a lot of people online when you posted the solution also , :smile:. Classic!
 
Last edited:
I found the solution for my own, not really waiting for anyone's solution alone,
I use definition of limit to start, then apply the inequality.
 

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