4.6.5 Chebyshev Bounds Video
PROFESSOR: Our topic is deviation from the mean, meaning the probability that a random variable returns a value that differs significantly from its mean. Now, the Markov bound gave you a course bound on the probability that R was overly large using very little information about R. Not surprisingly, if you know a little bit more about the distribution of R, simply that it's not negative, you can state tighter bounds. And this was noticed by a mathematician named Chebyshev. And he has a bound called the Chebyshev bound. Now, it's interesting that the Markov bound, even though it's very weak and seems not very useful, the Chebyshev bound, which generally gives you a significantly stronger, invaluably stronger bound on the probability that a random variable differs much from its mean is actually a trivial corollary of Markov theorem. So that's just a very simple ingenious way to use Markov's bound to derive Chebyshev bound. And let's look at how. So we...