Deriving Expectations from Formulas: (y1,y2) Distribution

[electronic engineer]

Hello,
we have the following example:

Assume that (y1,y2) are discrete valued and follow such a distribution that the pair are with probability 1/4 equal to any of the following cases: (0,1),(0,-1),(1,0),(-1,0) .


E{y1^2*y2^2}=0
E{y1^2}*E{y2^2}=1/4
I don't understand how the expectations were derived . Could anyone help?

Thanks in advanced!

 

[tiny-tim]

Hello electronic engineer!

(try using the X² and X₂ icons just above the Reply box )

E{y1^2*y2^2}=0
E{y1^2}*E{y2^2}=1/4

easy! … y₁²y₂² is always 0, isn't it, so its expectation must be 0

and y₁² is 0 0 1 and 1 with probability 0.25 each, so its expectation is 0.5

 

[electronic engineer]

I know but I thought this is only an informal answer :)