Suan-Aik Yeo I agree with the response that you have posted for part a. But I am unsure whether or not part b is correct. I mean the symmetry makes sense but will this make them all equal?? I am not sure.
//Suan: Well, I'm pretty sure that the PDF is exactly the same: think about it: Y is more likely to be filled in when y > 0.5. Same goes for X: X is more likely to be filled in when X > 0.5. So, going from there, E[Y] should also be exactly the same, from the formula, and from THAT, the variance should also be the same (also from the variance formula).
