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Random Variables and Statistical Analysis

X and Y are random variables.
What are the marginal pdfs of (x+y) (where 0<x<1 and 0<y<1)?
What is the expectation, covariance, correlation and and covariance coefficient?
What are the joint and marginal pdfs and cdfs?

(ii) Also,differently - if Fx|y(x|y) is constant over the 0 to 1. What is Fy|x(y|x)? (is there enough information to determine this?)

(iii) X and Y are random variables
Z=XY (x and y: X^2+y^2<=1)
What is the cdf, pdf, expectation, and variance?

Thanks. Please answer the first one. The second and third may not have enough information. If not, then please explain the relationship between Fx|y(x|y) and Fy|x(y|x) in ii and how to find the cdf, pdf, etc of Z when Z is a product function of two random variables.

Please provide whatever information you can from the information provided here (on any of the problems). I'm looking for insight.

Solution Summary

This solution has step-by-step calculations to determine the marginal pdf, expectation, covariance, correlation and covariance coefficient. All formulas and workings are shown.