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dubeypuja

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In summary, the expectation of the product of three random variables (RVs) is the average value that would be obtained if the product of the three RVs were repeatedly calculated over an infinite number of trials. It is calculated by multiplying the individual expectations of each RV and provides information about their relationship and interaction. There are several properties of the expectation of the product of three RVs, including linearity and independence. This concept has many practical applications in fields such as finance, economics, and engineering, and is commonly used in statistical models and simulations to make predictions and inform decision-making.

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dubeypuja

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pasmith

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dubeypuja said:But A & C are the same random variable

So isn't [itex]\mathbb{E}(ABC) = \mathbb{E}(A^2B) = \mathbb{E}(A^2)\mathbb{E}(B)[/itex]?

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The "Expectation of Product of three RVs" refers to a mathematical concept in probability and statistics that calculates the average value of the product of three random variables. It is a measure of central tendency that helps to understand the relationship between three variables and their combined effect.

The "Expectation of Product of three RVs" is calculated by multiplying the individual expectations of each random variable. In other words, it is the product of the expected values of the three variables. This can be represented mathematically as E[XYZ] = E[X] * E[Y] * E[Z].

The "Expectation of Product of three RVs" is a useful tool in research as it helps to understand the relationship between three variables and their combined effect. It can also be used to make predictions and draw conclusions about the variables in a given system.

The "Expectation of Product of three RVs" and "Product of Expectations of three RVs" may sound similar, but they are different concepts. The former calculates the average value of the product of three random variables, while the latter calculates the product of the expected values of three variables. In other words, the "Expectation of Product of three RVs" takes into account the variability of the variables, while the "Product of Expectations of three RVs" does not.

The "Expectation of Product of three RVs" has various applications in fields such as finance, engineering, and physics. For example, it can be used in risk assessment and portfolio management in finance, in predicting the strength of materials in engineering, and in understanding the behavior of particles in physics.

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