Meaning of Independent Identically distributed random variables

  • Thread starter dionysian
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  • #1
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Main Question or Discussion Point

I am a little fuzzy on the meaning of Independent Identically distributed random variables. I understand the independent part but still not 100% on the identically distributed part. I understand that identically distributed means they have the same pdf and cdf but does this mean that they have the same mean and variance?

For example if i have a sequence of random variables: N(0,1),N(2,4),N(3,5) and they are all independent are they IID?
 

Answers and Replies

  • #2
jav
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If they have the same pdf, then they by definition have the same mean and variance.
 
  • #3
mathman
Science Advisor
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For example if i have a sequence of random variables: N(0,1),N(2,4),N(3,5) and they are all independent are they IID?
They are all normal, but since the parameters are different, the distribution functions are different. (Not IID, only I).
 
Last edited:
  • #4
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Thanks.
 

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