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Are random variables based on the same pmf or pdf always independent?

  1. Jul 25, 2013 #1
    Are they always independent from each other so that you can multiply their E[X] together to form another E[X] with the same distribution and pmf or pdf?
     
  2. jcsd
  3. Jul 25, 2013 #2

    jbunniii

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    No, in general they need not be independent. In the most extreme case, you may have something like X = some random variable, and Y = X. Then X and Y are 100% correlated, so they are certainly not independent.
     
  4. Jul 25, 2013 #3
    How do you verify their independence then? Any quick and easy way? Any obvious cases?
     
  5. Jul 25, 2013 #4

    chiro

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    Hey EdmureTully.

    The condition for independence between random variables is P(A = a, B = b) = P(A=a)*P(B=b) where the left hand side is the joint distribution.

    If you have this separability, then the two random variables are by definition independent.
     
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