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Furthermore, part of it might be because of the word "expectation." In common usage, when we expect something to happen, we think it's more likely to happen than not. But in probability, that's clearly not the case, because we're taking a weighted average of possible outcomes, and the weighted average itself might be an unlikely, or even impossible outcome. This aspect of Expectation Wiktionary The Free Dictionary plays a vital role in practical applications.
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This may seem trivial but just to confirm, as the expected value is a constant, this implies that the expectation of an expectation is just itself. It would be useful to know if this assumption is. This aspect of Expectation Wiktionary The Free Dictionary plays a vital role in practical applications.
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Moreover, part of it might be because of the word "expectation." In common usage, when we expect something to happen, we think it's more likely to happen than not. But in probability, that's clearly not the case, because we're taking a weighted average of possible outcomes, and the weighted average itself might be an unlikely, or even impossible outcome. This aspect of Expectation Wiktionary The Free Dictionary plays a vital role in practical applications.
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