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Uniform distribution - Independent Randmo variables?

  1. May 14, 2012 #1
    Hi guys,

    I have this doubt but i am not sure, if i have an uniform distibution can i conclude that the events or random variables are independent?

    Thank you
     
  2. jcsd
  3. May 14, 2012 #2
    Could you please explain a little bit more about your data? How many random variables? Which of those variables are uniform...
     
  4. May 14, 2012 #3

    mathman

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    No. For example choose a random variable X from a uniform distribution (0,1) and then let
    Y = 1 - X. X and Y are certainly not independent, but both have unform distributions.
     
  5. May 15, 2012 #4
    Generally, distribution without any additional information (e.g. parameters in some dists.) doesn't say anything about dependence. Uniformity of random variable only means, that its realizations are equiprobable, that is [itex]\mathbb{P}[X=x_1] = \mathbb{P}[X=x_2] = ...[/itex] where [itex]X \sim U(a,b)[/itex] and [itex]x_i \in [a,b][/itex]. The notion of (in)dependence is much more tricky. Are you talking about multiple uniformly distributed random variables? A nice example of correlated uniformly distributed rvs gave mathman.
     
  6. May 15, 2012 #5

    chiro

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    The test that will definitely tell if two variables are dependent is if E[XY] <> E[X]E[Y] for two variables X and Y.

    The converse is not true though funnily enough: you can show that E[XY] = E[X]E[Y] but still have instances where you have dependent variables, although the case that this happens provides a kind of 'evidence' that they are independent (doesn't mean its conclusive though).
     
  7. May 19, 2012 #6
    Thanks to all. So i think the best way to look for it is the test that mentioned chiro.
     
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