Probability independent variable question

[robertdeniro]

Homework Statement

if X and Y are independent random variables

does it imply that X^2 and Y^2 are also independent?

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

hi robertdeniro!

(try using the X² tag just above the Reply box )

Tel us what you think, and why, and then we'll comment!

 

[robertdeniro]

i think X² and Y² are also independent because

E(XY)=E(X)E(Y)

so E(X²Y²)=E(X²)E(Y²) ?

 

[tiny-tim]

i think X² and Y² are also independent because

E(XY)=E(X)E(Y)

so E(X²Y²)=E(X²)E(Y²) ?

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. ​