# can chernoff bounds be used for proving upper bounds as well as lower bounds

I have a hw problem where it is asked to show theta(n) using chernoff bounds. I am able to prove for O(n) but not in the reverse way.Is it possible to prove both bounds using chernoff?

-
What is the context? For eg, what is the hw problem? –  Aryabhata Mar 12 '12 at 0:19
What is theta(n)? What is O(n)? Also, please add the homework tag since this is homework. –  Dilip Sarwate Mar 12 '12 at 0:22

Let $X_{1}, ..., X_{n}$ be independent Bernoulli random variables, each having probability $p > 1/2$. Then the probability of simultaneous occurrence of more than $n/2$ of the events has an exact value $P$.
$P \geq 1 - e ^{-2n(p-\frac{1}{2})^2}$