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whitehorsey
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Does μ_{x} mean the same thing as E[X]? Also, does σ^{2}_{x} mean the same thing as Var X?
haruspex said:Those would be reasonable notations for E[X], Var(X). I wouldn't say it's sufficiently standard to answer more confidently.
Expected value, also known as mean or average, is a measure of the central tendency of a probability distribution. It represents the average outcome of a random variable over a large number of trials.
To calculate the expected value, multiply each possible outcome by its probability of occurring and sum up all the products. This formula is also known as the weighted average formula.
Expected value can represent the long-term average outcome of a situation with random or uncertain outcomes. For example, it can be used in decision-making processes such as investment analysis or risk assessment.
Variance is a measure of the spread or variability of a probability distribution. It represents how far the values of a random variable are spread out from the expected value.
Variance is calculated by taking the sum of the squared differences between each outcome and the expected value, multiplied by their respective probabilities. In other words, variance measures how much the actual outcomes deviate from the expected value.