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Thread: independent random variables

  1. #1
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    independent random variables

    Hi,
    I am looking for an example of mutually independent random variables that are not k-wise independent.

    https://en.wikipedia.org/wiki/Pairwise_independence

    Mutually (Jointly) Independent Events

    Thanks in advance
    Last edited by hedi; May 7th 2017 at 03:18 PM.
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  2. #2
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    Re: independent random variables

    Quote Originally Posted by hedi View Post
    I am looking for an example of mutually independent random variables that are not k-wise independent.
    https://en.wikipedia.org/wiki/Pairwise_independence
    Mutually (Jointly) Independent Events
    I am confused. The links you posted actually shows that you look in vain,
    "Thus, by the definitions, mutual independence implies the pairwise independence." is the first sentence in one of them.

    Do you want to re-phrase your question? Or tell us how I have miss-read it?
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  3. #3
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    Re: independent random variables

    I think he means you have a set of events $e_i$, such that $\forall i,j\neq i,~e_i,~e_j$ are independent yet the joint pdf is not a product of all the marginals.

    This link has some examples
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