16 Apr
2013
16 Apr
'13
10:36 p.m.
--True, but the expectation = harmonic(n) formula works without need of independence.
Yes, expectation doesn't require independence.
I think Moore's point is this independence comes in handy when working on higher moments than the 1st.
yes.
--k-tuples of what? The i_1,..., i_k need to be selected from {1,2,3...,n} without replacement, I think is what he meant.
yep.
where we start with all 3-tuples, remove the ones where one i equals the other two,
--he meant "remove the ones with two i's equal"
oops, yes. thanks. regarding the generalization to larger k: cool. I need to read up on my Stirling numbers. There's an inclusion-exclusion formula here... alternately, we could compute the k'th moment E[t^k] directly as (z d/dz)^t G(z) at z=1. Cris