1. In class we defined the statistical (also known as variational) distance between two distributions A and B taking values in U to be |A− B| = maxT⊆U |Pr[A ∈ T ]− Pr[B ∈ T ]|. A× B denotes the distribution on (a, b) obtained by independently picking a according to A and b according to B. (A,B) denotes some random variable on U × U with marginal distributions A and B. For f : U → U ′ and A that...