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.

if you rewrite the equation as $P(Y = x) = xP(X = x)/\lambda$, then the distribution of $Y$ is called the length-biased distribution for $X$. it arises, for example, if one has a bunch of sticks in a bag and reaches in and selects one at random - where the probability a particular stick is selected is proportional to its length. if the lengths of the sticks are realizations of the random variable $X$, the distribution of the length of the selected stick is that of $Y$.
