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marginal pdfs of simple random samples with replacement

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If a questions asks us to take a random sample of three observations from a population, where each observation in the sample is chosen by a random draw from the entire population and we have to find marginal pdfs of $X_1, X_2, X_3$, wouldn't that be redundant since $X_1, X_2, X_3$ would be the same?

I am confused as to how $X_1, X_2, X_3$ would different from each other. I'm not sure if I am misunderstanding the concept as a whole/doing it wrong, or the professor just wanted us to take the same marginal pdfs multiple times... Could someone walk me through this?

probability statistics random-variables

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asked Mar 27 at 20:20

qhandqhand

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  I think it depends on what the definitions of $X_1, X_2$ and $X_3$ are.
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  – callculus
  Mar 27 at 20:27
  

  
  
  
  


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  @callculus if the population is of size 8, and R is 26, 26, 26, 38, 38, 38, 96, 96. Wouldn't $X_1, X_2, X_3$ just be 26, 38, 96, hence the same?
  $endgroup$
  – qhand
  Mar 27 at 22:50
  

  
  
  
  


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  I think what callculus is meaning is that you haven't defined $X_1$, $X_2$ or $X_3$, and also haven't $R$.
  $endgroup$
  – Sam T
  Mar 28 at 0:11
  

  
  
  
  


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  @SamT I don't think I'm understanding how to do it then. With given information of population size and R, how would I calculate $X_1, X_2, X3$?
  $endgroup$
  – qhand
  Mar 28 at 1:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What is $X_1$? $R$?
  $endgroup$
  – Sam T
  Mar 28 at 8:57
  

  
  
  
  

 | 
show 1 more comment

0

$begingroup$

If a questions asks us to take a random sample of three observations from a population, where each observation in the sample is chosen by a random draw from the entire population and we have to find marginal pdfs of $X_1, X_2, X_3$, wouldn't that be redundant since $X_1, X_2, X_3$ would be the same?

I am confused as to how $X_1, X_2, X_3$ would different from each other. I'm not sure if I am misunderstanding the concept as a whole/doing it wrong, or the professor just wanted us to take the same marginal pdfs multiple times... Could someone walk me through this?

probability statistics random-variables

share|cite|improve this question

asked Mar 27 at 20:20

qhandqhand

1

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I think it depends on what the definitions of $X_1, X_2$ and $X_3$ are.
  $endgroup$
  – callculus
  Mar 27 at 20:27
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @callculus if the population is of size 8, and R is 26, 26, 26, 38, 38, 38, 96, 96. Wouldn't $X_1, X_2, X_3$ just be 26, 38, 96, hence the same?
  $endgroup$
  – qhand
  Mar 27 at 22:50
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I think what callculus is meaning is that you haven't defined $X_1$, $X_2$ or $X_3$, and also haven't $R$.
  $endgroup$
  – Sam T
  Mar 28 at 0:11
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @SamT I don't think I'm understanding how to do it then. With given information of population size and R, how would I calculate $X_1, X_2, X3$?
  $endgroup$
  – qhand
  Mar 28 at 1:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What is $X_1$? $R$?
  $endgroup$
  – Sam T
  Mar 28 at 8:57
  

  
  
  
  

 | 
show 1 more comment

$begingroup$

If a questions asks us to take a random sample of three observations from a population, where each observation in the sample is chosen by a random draw from the entire population and we have to find marginal pdfs of $X_1, X_2, X_3$, wouldn't that be redundant since $X_1, X_2, X_3$ would be the same?

I am confused as to how $X_1, X_2, X_3$ would different from each other. I'm not sure if I am misunderstanding the concept as a whole/doing it wrong, or the professor just wanted us to take the same marginal pdfs multiple times... Could someone walk me through this?

probability statistics random-variables

share|cite|improve this question

asked Mar 27 at 20:20

qhandqhand

1

$endgroup$

share|cite|improve this question

asked Mar 27 at 20:20

qhandqhand

1

share|cite|improve this question

asked Mar 27 at 20:20

qhandqhand

1

asked Mar 27 at 20:20

qhandqhand

1

asked Mar 27 at 20:20

qhandqhand

1