(15 points) For each of the functions of the continuous joint random variables(X,Y) below, (1)sketch the region of the plane corresponding to the following events (positive and negative)(2) state whether

the events are product form (3) give the double integral with limits of integration, ie, choose the limits a, b. c. and d below. \int_{a}^{b} \int_{c}^{d} f_{X, Y}(x, y) d x d y \{X-Y \leq 2\} \{\max (X-Y)<6\} \{|X|<|Y|\} \{|X-Y| \leq 2\} \{X / Y \leq 1\}