- #1
robertdeniro
- 37
- 0
Homework Statement
if X and Y are independent random variables
does it imply that X^2 and Y^2 are also independent?
Probability independent variable question
- Thread starter robertdeniro
- Start date
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Homework Help Overview
The discussion revolves around the independence of random variables, specifically questioning whether the independence of two random variables X and Y implies that their squares, X² and Y², are also independent. The subject area is probability theory.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants explore the relationship between the independence of X and Y and the independence of their squares, with some suggesting that the expectation values can be used to infer independence. Others challenge this reasoning, emphasizing the need for a proof based on probabilities rather than expectations.
Discussion Status
The discussion is active, with participants sharing their thoughts and questioning the validity of using expectation values to prove independence. There is a clear divergence in approaches, with some advocating for a probabilistic proof while others are still considering the implications of expectation values.
Contextual Notes
Participants are encouraged to provide their reasoning and engage in a dialogue about the assumptions underlying the problem, particularly regarding the definitions of independence in the context of random variables.
if X and Y are independent random variables
does it imply that X^2 and Y^2 are also independent?
- #2
tiny-tim
Science Advisor
Homework Helper
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hi robertdeniro! 
(try using the X2 tag just above the Reply box
)
Tel us what you think, and why, and then we'll comment!
(try using the X2 tag just above the Reply box
)Tel us what you think, and why, and then we'll comment!
- #3
robertdeniro
- 37
- 0
i think X2 and Y2 are also independent because
E(XY)=E(X)E(Y)
so E(X2Y2)=E(X2)E(Y2) ?
E(XY)=E(X)E(Y)
so E(X2Y2)=E(X2)E(Y2) ?
- #4
tiny-tim
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robertdeniro said:
Nooo
… why would E(AB) = E(A)E(B)? 
You must prove independence by considering probabilities, not expectation values …
find a proof that involves P, not E.