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

  • Thread starter Jekertee
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In summary, the conversation discusses how to prove that the limit of the expectation of samples x_i, with i from 1 to m, is equal to the given limit x_m=n. The solution is found using the definition of limit and applying an inequality. However, it is important to note that providing complete solutions for homework problems is not allowed on this forum.
  • #1
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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  • #2
EDIT: Solution removed
 
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  • #3
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.
 
  • #4
: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!
 
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  • #5
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.
 

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

What does "lim x_m=n" mean?

"lim x_m=n" represents the limit of a sequence, where x_m is the mth term in the sequence and n is the limit of the sequence as m approaches infinity.

How do you find the limit of a sequence?

To find the limit of a sequence, you need to evaluate the sequence as m approaches infinity. This can be done by finding the pattern of the sequence and observing what value it approaches as m gets larger and larger.

What is the significance of finding the limit of a sequence?

The limit of a sequence tells us the behavior of a sequence as the number of terms approaches infinity. It helps us understand if the sequence will converge (approach a finite value) or diverge (approach infinity).

Are there any specific methods for finding the limit of a sequence?

Yes, there are various methods for finding the limit of a sequence such as using the squeeze theorem, the ratio test, or the root test. The method used depends on the type of sequence being evaluated.

Can the limit of a sequence be undefined?

Yes, the limit of a sequence can be undefined if the sequence does not approach a finite value or infinity as m approaches infinity. In this case, the limit does not exist.

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