Expectation

Expectation or Expectations may refer to: To do or be someone or something in another ones point of view.

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Expectation (Waltz)

"Expectation" (Russian: ожидание) is a melancholy and solemn waltz composed in 1980 by Ilya Herold Lavrentievich Kittler.

The origin of this piece is nebulous, as many Klezmer orchestras know this song as a Jewish piece and plenty of Russians claim this is a Soviet Army song. An even less well known song that goes by the name Awaiting uses the same melody with Russian lyrics. The original version of the song was written in E minor while the Klezmer version for the accordion and clarinet is in D Minor. Expectation is mostly made of minor notes along with relative minor thirds and sub-4th octaves, adding to its solemnity.

This piece has been featured in many places, such as the Russian film "The Optimistic Tragedy" and a famous Klezmer player Dave Tarras' album Freilach in Hi-Fi. Most of these appearances do not list the true song's name. However, plenty of sheet music appears online for the song, mainly for accordion.

Expected value

In probability theory, the expected value of a random variable is intuitively the long-run average value of repetitions of the experiment it represents. For example, the expected value of a six-sided die roll is 3.5 because, roughly speaking, the average of an extremely large number of die rolls is practically always nearly equal to 3.5. Less roughly, the law of large numbers guarantees that the arithmetic mean of the values almost surely converges to the expected value as the number of repetitions goes to infinity. The expected value is also known as the expectation, mathematical expectation, EV, average, mean value, mean, or first moment.

More practically, the expected value of a discrete random variable is the probability-weighted average of all possible values. In other words, each possible value the random variable can assume is multiplied by its probability of occurring, and the resulting products are summed to produce the expected value. The same works for continuous random variables, except the sum is replaced by an integral and the probabilities by probability densities. The formal definition subsumes both of these and also works for distributions which are neither discrete nor continuous: the expected value of a random variable is the integral of the random variable with respect to its probability measure.