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Joint and marginal distribution functions

I am having troubles with #2 part (b) in the attached document. In part (a) I found what I believe to be the joint distribution for the transformation. I am questioning my interval for T (domain) for this joint distribution however. To complete part (b) it will be necessary to take the integral of the joint in part (a) with respect to Y1 with the appropriate limits of integration in terms of Y2. Finally this marginal pdf will need to be identified (gamma, beta, normal, chi-square, etc.) with whatever parameters it may have.

Problem #1 is also on this sheet which I completed with satisfaction and could be used possibly as a model to aid in solving this.

See attached file for full problem description.