normal distributed proc.

[Petrarca]

Let Y~N(0,1) (i.e Y is a random variable) and Z=Y if -Z<=Y<=Z or -Y otherwise.

I would like to show two things.

1.) E[ZY] and if Y and Z are dependent or not.

1.) E[ZY]=? E[Y^2]=y
2.) Are there sets A, B such that P(Y\inA and Z\inB)=P(Y\inA)*P(Z\inB) or not?

 

[aaronhotchner]

Maybe I'm missing something, but how do you determine "if -Z <= Y <= Z" without a definition for Z?

Either way, the question of whether Y and Z are dependent is pretty obviously yes, since you're classifying Z as either Y or -Y.

 

[Petrarca]

I only know that Y~N(0,1) and Z is defined by

Z=Y if Z <= Y <= Z
Z=-Y otherwise

So how is it possible to compute E[ZY]?

P.S: Can you give exmaples of sets A,B, such that P(Y\inA and Z\inB)=P(Y\inA)*P(Z\inB) does not hold?

 

[Ito]

I think you are exploiting the forum to solve your homework problems