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find Kullback-Leibler Divergence distance between P and Q (2-dimensional probability distribution)

Suppose we have two 2-dimensional probability distributions, P and Q: o V(x,y) E P,x = 0 and y~U(0,1) o V(x,y) E Q): = 9,0 5 6 5 Land y~U(0,1) 6 is a given constant. Obviously, when 6 0, there is no overlap between P and Q. a. For the case where 9 0, calculate the distance between P and Q by each of the three measurements. b. Repeat section a for the case where 6 = 0. c. Following your answers, what is the advantage of the Wasserstein Distance over the previous two? . KL (Kullback-Leibler Divergence): p(x) DKL (pllq) = p(x) log dx XEX q(x)