Solution:
Consider the transformation from (x, y) to (t, w) given by t = x + y and w = x. (It may seem redundant to make up the new name "w" for x, but this makes it easier to distinguish between the "old" variables x, y and the "new" variables t,w.) Correspondingly, consider the transformation from (X, Y) to (T, W) given by T = X + Y, W = X. Use the Jacobian to find the joint PDF of T, W and integrate out W to get the marginal PDF of T.

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