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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?

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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

1 Answer 1

It looks like it works in both directions. I never used it in the case of lower bound, but here Chernoff bound you can find example of usage as lower bound.

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 $P$.

The Chernoff bound shows that P has the following lower bound.

$P \geq 1 - e ^{-2n(p-\frac{1}{2})^2}$

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