Hi all, just a quick question here - the setup is as follows: X is a random variable, where and for constants c, n (n "large" here). I wish to show that . I've been told to use "Chernoff-esque bounds" here; however, after teaching myself a little about Chernoff bounds I haven't found a way to make this work - I know conceptually they're used to get upper bounds on the probability of 'tail events', and I can see that the multiplicative form could be useful but I haven't yet figured out how to translate the bounds which I've found online into a workable form for this problem (I've never used Chernoff bounds before!).
I'm told observing the fact that might also help, so I suspect maybe what we really need is to show is but as I said, no luck so far since I can't prove step if indeed that is the way to do it. I suspect that this result only needs a few lines of work once you have the bound you require from Chernoff, so if anyone could show me how to do this I'd be very grateful! -Sim