Using Joint Distributions and conditional probabilities

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7 question exercise

This exercise is particularly confusing me because I do not understand the distribution of 'X-Y' or how to calculate the probabilities

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$$\mathbb P\{X-Y<a\}=\iint_{\{(x,y)\mid x-y<\alpha \}}f_{X,Y}(x,y)\mathrm dx\mathrm dy.$$