Expectation of Product of three RVs

[dubeypuja]

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}?

 

[pasmith]

But A & C are the same random variable

So isn't $\mathbb{E}(ABC) = \mathbb{E}(A^2B) = \mathbb{E}(A^2)\mathbb{E}(B)$?

 

[FactChecker]

Do you mean that A and C always have the same value or that they are two distinct, independent, identically distributed random variables?