Is there any known bound on sum of independent but not identically
distributed geometric random variables?
I have to show that the tail of the sum drops exponentially (like in
the Chernoff bounds for the sum of iid geom. variables).


Formally, if $X\_i$ ~ Geom($p\_i$), and $X = \sum\_{i=1}^n X\_i$, and it is known that $E[X]=\Theta(n)$,


Is it possible to show that $\Pr(X < 2E[X]) > 1 - \delta ^n$, where $\delta < 1$? 



Probability Theory, Chernoff Bounds, Sum of Independent (but not identically distributed) r.v
This isn't true, in general. If you take $p\_0=1/n$ and the other $p\_i=1$ then you get a constant probability for $X>2\mathbb{E}(X)$.


