1:45 PM
If a collection $A_i:i\in I$ of events indexed by a nonempty index set I is
mutually independent, then the collection is also pairwise independent. But How can I prove that?

2:09 PM
@ElizabethJ.Magee Trivial.

3 hours later…
5:16 PM
@DavidP Adding Sum[k∈{0..2n}] n·C(2n,k) = n·2^(2n) gives n·2^(2n) = 2 · Sum[k∈{0..n}] k·C(2n,k). First counting: Pick S⊆{1..2n} and pick x∈{1..2n}, and change S to {1..2n}∖S if needed to make #(S)<n or ( #(S)=n and x∈S ). The change step double-counts hence 2^(2n)·2n/2. Second counting: Too lazy but it seems almost done. =P