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Text Box: North Shore Computing Text Box: Documentation beats conversation, the numbers don’t lie… Text Box: Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. In probability theory, the expected value (or expectation, or Mathematical Expectation) of a random variable is the weighted average of all possible values that this random variable can take on. From a rigorous theoretical standpoint, the expected value is the integral of the random variable with respect to its probability measure. The expected value may be intuitively understood by the law of large numbers. The Law of Large Numbers is a theorem that describes the result of executing the same strategy a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the mathematical expectation, and will tend to become closer as more trials are performed. This expectation, when it exists, is almost surely the limit of the sample mean as sample size grows to infinity. More informally, it can be interpreted as the long-run average result of many independent repetitions for a given strategy. It is these repetitions that decisively conclude or deny strategy profitability... Text Box: Simply stated:

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