i need to solve

Exercise 1. Consider the two sequences of measures = 01-2- and Un = 16_1+ (1 - 1)61. From the mere look of it one would guess that both of these sequences approach the measure * = 6, in some way. The KL divergence KL(ulu) from u to v is defined as oo if there is an r with u(r) > 0 and v(x) = 0 and KL(uv) = _ "(x) log H(I) v(I) IEsupp(#) otherwise. (i) Calculate KL(#|An) and KL(#|Un). Do the sequences , and v., converge to a w.r.t. the KL-divergence? L.e. do the sequences KL(#|An) and KL(m V,) approach 0? (ii) For each /,, and v, find the optimal coupling T between An (resp. un) and n with the procedure from Example 2.29 (by hand). The Wasserstein-2 distance is then given as W(T) = L., tula, - a, ?. Do the sequences un and Un converge to a in the Wasserstein-2 distance