Relationship between these two probability mass functions 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.

I don't have enough reputation yet, or this would be a comment.
A random variable can have only one probability mass function, so it is not clear what you are asking.  Where do these equations come from?
