Chebyshev's inequality pdf file

Cs 70 discrete mathematics and probability theory fall 2015 lecture 18 chebyshevs inequality problem. With only the mean and standard deviation, we can determine the amount of data a certain number of standard deviations from the mean. This method allows for detection of multiple outliers, not just one at a time. Neal, wku math 382 chebyshevs inequality let x be an arbitrary random variable with mean and variance. Chebyshev s inequality, also known as chebyshev s theorem, is a statistical tool that measures dispersion in a data population. A wellknown theorem proved by the russian mathematician chebyshev pronounced just as it. Chebyshevs inequality example question cfa level i.

Proof of the chebyshev inequality continuous case given. Cs 70 discrete mathematics and probability theory fall. Mildorf december 22, 2005 it is the purpose of this document to familiarize the reader with a wide range of theorems and techniques that can be used to solve inequalities of the variety typically appearing on mathematical olympiads or other elementary proof contests. Cs 70 discrete mathematics and probability theory fall 2009 satish rao,david tse lecture 15 variance question. University probability mean and variance of sums, chebyshevs inequality resolved i have a list of questions which i cant really ask anywhere else, so im hoping i can get most answered. Chebyshevs inequality allows us to get an idea of probabilities of. One tailed version of chebyshevs inequality by henry.

The above inequality is the most general form of the 2sided chebyshev. Chebyshev inequalities for products of random variables. For these cases, an outlier detection method, using the empirical data and based upon chebyshevs inequality, was formed. Chebyshevs inequality for a random variable x with. Lecture 19 chebyshevs inequality limit theorems i x. Quantum chebyshev inequality our main contribution theorem 3. However, we can use chebyshev s inequality to compute an upper bound to it. Chebyshevs inequality is one of the most common inequalities used in prob ability theory to bound the tail probabilities of a random variable x ha ving. It can be used with any data distribution, and relies only on the.

Pdf data outlier detection using the chebyshev theorem. Cs 70 discrete mathematics and probability theory variance. Quantum chebyshevs inequality and applications irif. However, chebyshevs inequality goes slightly against the 689599. Chebyshevs inequality is one of the most common inequalities used in prob. For example, if the mean age of a certain population is known to be. Some extra thoughts on chebyshev type inequalities for unimodal distributions october 1999. If x is a continuous random variable with a unimodal probability density function pdf, we may be able to tighten chebyshevs inequ ality, though only by adding some complexity. The most elementary tail bound is markovs inequality, which asserts that for a positive random variable x.