Expectation of Product of three RVs

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The discussion focuses on calculating the expectation E{ABC} for three random variables A, B, and C, where A and B are independent, B and C are independent, and A and C are identical random variables with the same distribution. Participants debate whether E{ABC} can be expressed as E{AE{B}C} and whether A and C being the same variable affects this calculation. There is clarification needed on whether A and C are treated as identical values or as two distinct but identically distributed random variables. The consensus leans towards understanding the implications of A and C's relationship on the expectation calculation. The conversation emphasizes the importance of independence and identical distribution in determining E{ABC}.
dubeypuja
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We have three Random variable or vector A,B,C. Condition is A & B are independent as well as B & C are independent RVs . But A & C are the same random variable with same distribution . So How can determine E{ABC}. Can I write this E{ABC}= E{AE{B}C}?
 
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dubeypuja said:
But A & C are the same random variable

So isn't \mathbb{E}(ABC) = \mathbb{E}(A^2B) = \mathbb{E}(A^2)\mathbb{E}(B)?
 
Do you mean that A and C always have the same value or that they are two distinct, independent, identically distributed random variables?
 
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