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If I have two different discrete distributions of random variables X and Y, such that their probability mass functions are related as follows:

$P(X=x_i) = \lambda\frac{P (Y=x_i)}{x_i} $

what can I infer from this equation? Any observations or interesting properties that you see based on this relation?

What if,
P($X=x_i$) = $\lambda\sqrt{\frac{P (Y=x_i)}{x_i} }$

In both cases, $\lambda$ is a constant.

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    It would be clearer to write this with two random variables and one measure $P$; i.e. $P(X = x_i) = \lambda P(Y=x_i)/x_i$. Also, "what can I infer" is very vague; what sorts of things would you like to infer?2010-11-04
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    @Nate:Any observation will do. I am applying a polynomial decay on a pmf to get another pmf. Something like 'A uniform Y will result in a geometric distribution(?) for X.'2010-11-04
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    Also on MathOverflow: http://mathoverflow.net/questions/44902/relationship-between-these-two-probability-mass-functions (repaired clipboard failure)2010-11-05

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