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Aug 2 at 15:59 comment added cinch Thanks, after discussing with you back and forth, I did myself thinking about the key role of projection function of vector space in linear algebra which is similar to primitive recursive projection function in computability theory related to Turing machine in computer science.
Aug 2 at 10:13 comment added spie227 Accepted your answer. I wanted to check whether there is a formal proof of this available online or did you derive this yourself? Thank you.
Aug 2 at 9:28 vote accept spie227
Jul 31 at 4:01 history edited cinch CC BY-SA 4.0
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Jul 31 at 3:28 comment added cinch After thinking about this subtle split-conditional pairwise independence more, I edited my answer significantly to address your reasonable intuition which was still not rigorously proved by your own proposed answer. Hope now everything is completely clarified including all your other related MLE questions!
Jul 31 at 3:19 history undeleted cinch
Jul 31 at 3:19 history edited cinch CC BY-SA 4.0
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Jul 30 at 22:10 history deleted cinch via Vote
Jul 28 at 17:42 comment added spie227 keeping notations aside, as @whuber pointed above, functions of independent random vectors are also independent. The joint distribution or "splitted" conditional distribution is a function of the said random vectors. Hence they ought to be independent as well.
Jul 28 at 6:51 history answered cinch CC BY-SA 4.0