Lecture 8-cs648-2013

Randomized AlgorithmsCS648

Lecture 8

Tools for bounding deviation of a random variable

• Markov’s Inequality

• Chernoff Bound

Markov’s Inequality and Chernoff bound were stated and proved in this lecture class in an interactive manner providing all intuition and reasoning for each step of the proof.

Markov’s Inequality

Chernoff’s Bound

Where to use:

If given random variable X can be expressed as a sum of n mutually independent Bernoulli random variables.

Homework

For various problems till now, we used our knowledge of binomial coefficients, elementary probability theory and Stirling’s approximation for getting a bound on the probability of error or probability of deviation from average running time. Try to use Chernoff’s bound to analyze these problems.

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