Statistic question

[statistic10]

Any ideea for this problem?
Let Z1,Z2 be independent standard normal r.v. and let ?:|?|<1 be a real number.Obtain the joint pdf of the random variables X=Z1,Y=?Z1+[sqrt(1-?^2)]Z2.

We don't know if X and Y are independent and I think Y has some distribution which I don't know what it is.
Thank you,
A frustrated student :idea:

 

[tkhunny]

Did you read the problem statement? You are GIVEN that they are Standard Normal and Independent.

Is rho a correlation or just some number?