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Homework Help: X1X2 ~ Y1Y2 if

  1. Sep 27, 2008 #1
    1. The problem statement, all variables and given/known data
    If X1 ~ Y1 and X2 ~ Y2, then X1X2 ~ Y1Y2, prove or find a counterexample. (the distribution of X1 has the same distribution of Y1 etc)


    2. Relevant equations
    -


    3. The attempt at a solution
    I'm guessing the statement is true. For example if X1 and Y1 were both uniform and X2 and Y2 are binomial, then a uniform * binomial is distributed the same as a uniform * binomial.
     
  2. jcsd
  3. Sep 27, 2008 #2

    HallsofIvy

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    It would help if you also told us what "~" meant.
     
  4. Sep 27, 2008 #3
    Ah sorry, it's the stuff I put in the brackets ie.

    X1 ~ Y1 : the distribution of X1 has the same distribution of Y1, X1 and Y1 being random variables.

    The same with X2 ~ Y2 and X1X2 ~ Y1Y2.
     
  5. Oct 5, 2008 #4
    If anyone was interested, the answer was no. The counter example was:

    Let [tex]P(X_1 = 1) = P(X_1 = -1) = 0.5[/tex]. Let [tex]X_2 = -X_1[/tex] and [tex]Y_1 = Y_2 = X_1. X_1 X_2 = -X_1^2 = -1[/tex] almost surely, but [tex]Y_1 Y_2 = X_1^2 = 1[/tex]
     
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