For any randomized trial, some variation from the mean is expected, of course, but the randomization ensures that the experimental groups have mean values that are close, due to the central limit theorem and Markov's inequality.

The term Chebyshev ’ s inequality may also refer to the Markov's inequality, especially in the context of analysis.

Markov's inequality states that for any real-valued random variable Y and any positive number a, we have Pr (| Y | > a ) ≤ E (| Y |)/ a.

One way to prove Chebyshev's inequality is to apply Markov's inequality to the random variable Y = ( X − μ )< sup > 2 </ sup > with a = ( σk )< sup > 2 </ sup >.

Common tools used in the probabilistic method include Markov's inequality, the Chernoff bound, and the Lovász local lemma.

Markov's inequality gives an upper bound for the measure of the set ( indicated in red ) where exceeds a given level.

In probability theory, Markov's inequality gives an upper bound for the probability that a non-negative function of a random variable is greater than or equal to some positive constant.

It is named after the Russian mathematician Andrey Markov, although it appeared earlier in the work of Pafnuty Chebyshev ( Markov's teacher ), and many sources, especially in analysis, refer to it as Chebyshev's inequality or Bienaymé's inequality.

An example of an application of Markov's inequality is the fact that ( assuming incomes are non-negative ) no more than 1 / 5 of the population can have more than 5 times the average income.

In the language of measure theory, Markov's inequality states that if ( X, Σ, μ ) is a measure space, ƒ is a measurable extended real-valued function, and, then

Chebyshev's inequality follows from Markov's inequality by considering the random variable

for which Markov's inequality reads

This identity is used in a simple proof of Markov's inequality.

If μ is less than 1, then the expected number of individuals goes rapidly to zero, which implies ultimate extinction with probability 1 by Markov's inequality.

* Markov's inequality and Chebyshev's inequality

Observe that any Las Vegas algorithm can be converted into a Monte Carlo algorithm ( via Markov's inequality ), by having it output an arbitrary, possibly incorrect answer if it fails to complete within a specified time.

* Markov's inequality, a probabilistic upper bound

By an application of Markov's inequality, a Las Vegas algorithm can be converted into a Monte Carlo algorithm via early termination ( assuming the algorithm structure provides for such a mechanism ).

It is a sharper bound than the known first or second moment based tail bounds such as Markov's inequality or Chebyshev inequality, which only yield power-law bounds on tail decay.

From Markov's inequality and using independence we can derive the following useful inequality:

For finite games, and games where the appropriate instance of Markov's rule can be constructively established by means of bar induction, then the non-constructive proof of a winning strategy for the first player can be converted into a winning strategy.

He made his debut for Plamen Markov's Bulgaria in a friendly against Spain on 20 November 2002, when he was a CSKA Sofia player, coming on as a second half substitute during 0 – 1 defeat at Los Cármenes in Granada.

By Markov's Inequality, the chance that it will yield an answer before we stop it is 1 / 2.

A single-move version of Markov's theorem, was published by.

This is nothing but Markov's inequality.

Bernoulli's inequality is often used as the crucial step in the proof of other inequalities.

The following inequality estimates the r-th power of 1 + x from the other side.

Not only does its value depend on income inequality within a country, its value depends on other factors such as the demographic structure.

Natural resources can add substantial's to a country's wealth, however a sudden inflow of money caused by a resource boom can create social problems including inflation harming other industries (" Dutch disease ") and corruption, leading to inequality and underdevelopment, this is known as the " resource curse ".

However, with quantum entanglement, if Alice and Bob measure the spin of their particles in directions other than just up or down, with the directions chosen to form a Bell's inequality, they can now observe a correlation that is fundamentally stronger than anything that is achievable in classical physics.

This dual nature of the Swazi economy, with high productivity in textile manufacturing and in the industrialized agricultural TDLs on the one hand, and declining productivity subsistence agriculture ( on SNL ) on the other, may well explain the country ’ s overall low growth, high inequality and unemployment.

In mathematics, the Cauchy – Schwarz inequality ( also known as the Bunyakovsky inequality, the Schwarz inequality, or the Cauchy – Bunyakovsky – Schwarz inequality, or Cauchy – Bunyakovsky inequality ), is a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, and other areas.

Moreover, Ireland's inequality persists by other measurements.

* comparative constructions expressing inequality: autre ( other ), meilleur ( better ), plus fort ( stronger ), moins intelligent ( less intelligent ), etc.

“ In the long term, therefore, fortified by increases in supplementary and other benefits under the Crossman regime in 1968 – 70, the welfare state had made some impact, almost by inadvertence, on social inequality and the maldistribution of real income ”.

The top example shows the case when there is a clear inequality and the bottom example shows the case when the third side, z, is nearly equal to the sum of the other two sides x + y.

In Euclidean geometry and some other geometries the triangle inequality is a theorem about distances.

With the exception of Ireland, the countries at risk of default in 2011 ( Greece, Italy, Spain, Portugal ) were notable for their high Gini-measured levels of income inequality compared to other European countries.

These first-wave anarcho-punk bands are musically varied but are often connected by discernible stylistic elements: a willingness to experiment that often went outside the bounds of other hardcore punk acts, a slipshod and improvised feeling, perhaps owing to the many of the bands conceiving of themselves more as musical collectives than formal acts, and " ranting " sections, where bands would expound on issues like animal rights or gender inequality.

) The Ligue des droits de l ' homme ( LDH, Human Rights League ) criticized the inequality before the law, under which Papon was freed while other prisoners did not have this luck.

Duos of equal importance on TV such as Kate McArdle and Allie Lowell ( Kate & Allie ), Oscar Madison and Felix Unger ( The Odd Couple ), Bret Maverick and Bart Maverick ( Maverick ), Captain Scarlet and Captain Blue ( Captain Scarlet and the Mysterons ), or Laverne De Fazio and Shirley Feeney ( Laverne & Shirley ), are sometimes both called sidekicks to each other, although the usual sense of the term denotes inequality.

In other words, an inequality of power among ethnic groups means " they are of such unequal power that one is able to impose its will upon another ".

As slavery is made illegal, other forms of inequality are addressed as well.

This campaign will encourage the North American Jewish community to examine the risks and rewards of peace for Israel and the Palestinians, and to undertake critical, constructive public dialogue on the most pressing social issues facing Israel today — including the status of Arab citizens of Israel and other minorities, as well as other issues of inequality and discrimination.