Skip to main content
Cross Validated

Return to Question

edited tags
Source Link
kjetil b halvorsen ♦
kjetil b halvorsen ♦
  • 82.8k
  • 32
  • 201
  • 663

Having read a little about exchangeability, I went back to thinking about the iid condition required for the central limit theorem. It struck me that if two random variables are drawn from an identical distribution, the occurrence of one event does not make it more or less probable for the occurrence of another event. I have no doubts that I am wrong and there is a reason why both independence and identical distribution are required. I just don't know why! Thanks very much!

Having read a little about exchangeability, I went back to thinking about the iid condition required for the central limit theorem. It struck me that if two random variables are drawn from an identical distribution, the occurrence of one event does not make it more or less probable for the occurrence of another event. I have no doubts that I am wrong and there is a reason why both independence and identical distribution are required. I just don't know why! Thanks very much!

Having read a little about exchangeability, I went back to thinking about the iid condition required for the central limit theorem. It struck me that if two random variables are drawn from an identical distribution, the occurrence of one event does not make it more or less probable for the occurrence of another event. I have no doubts that I am wrong and there is a reason why both independence and identical distribution are required. I just don't know why!

Question Protected by whuber♦
Tweeted twitter.com/#!/StackStats/status/132054116632506368
Source Link
HFC
HFC
  • 131
  • 1
  • 4

If random variables are drawn from an identical distribution, why doesn't this guarantee they are independent?

Having read a little about exchangeability, I went back to thinking about the iid condition required for the central limit theorem. It struck me that if two random variables are drawn from an identical distribution, the occurrence of one event does not make it more or less probable for the occurrence of another event. I have no doubts that I am wrong and there is a reason why both independence and identical distribution are required. I just don't know why! Thanks very much!