MATHEMATICAL EXPECTATION Meaning and
Definition
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Mathematical expectation is a statistical concept that refers to the expected value or outcome of a random variable. It is a measure used to determine the average result of an event over a large number of trials. Also known as the expected value or mean, the mathematical expectation provides a way to quantify the long-term behavior or average outcome of a random experiment.
Mathematical expectation is calculated by multiplying each outcome of a random variable by its associated probability and summing up these products. In other words, it is the sum of the products obtained by multiplying the value of each possible outcome by its corresponding probability of occurrence.
The mathematical expectation is particularly useful because it can be used to make predictions about the future behavior of a random variable. By studying the expected value, one can gain insights into the most likely outcome of an event, which can be valuable in various fields such as finance, insurance, and gambling.
It is important to note that the mathematical expectation is a theoretical concept and may not always match the actual outcome of a specific trial or experiment. However, over a large number of trials, the average of the observed outcomes will tend to converge towards the mathematical expectation.
Common Misspellings for MATHEMATICAL EXPECTATION
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Etymology of MATHEMATICAL EXPECTATION
The word "mathematical" originates from the Greek word "mathēma", meaning "science" or "knowledge", and the suffix "-ical", which is derived from the Latin suffix "-icus" and means "related to" or "pertaining to".
The term "expectation" comes from the Latin word "expectatio", which means "waiting" or "anticipation". It is derived from the verb "expectare", meaning "to look out for" or "await".
In the context of mathematics, the concept of "expectation" refers to the anticipated value or outcome of a random variable or a statistical experiment. It represents the average value that is expected to be obtained from a series of trials or events.
