RE: WG ACTION: 2 weeks to discuss [LL62] Do not space probes randomly

Stuart makes the point that throwing dices several times in sequence
makes the sum more predictable. That is however not entirely true. The
law of big numbers predicts that the standard deviation of the average
is inversely proportional to the square root of the number of trials.
However, we are not concerned here with the value of the average, but
rather with the value of the sum. According to the law of big numbers,
the standard deviation of the sum does not decrease: it increases
proportionally to the square root of the number of trials. 

In the case of N trials between 0 and 1 (first trial) or between 0.5 and
1.5 (successive trials) the average total delay will be 0.5*(N-1)+0.5*N
= (N-1)+0.5; the average variance of this total delay will be N/4; the
standard deviation of the last trial will be sqrt(N)/2.

In the case of N trials where the first one is randomized between 0 and
1 and the later ones repeated 1 second after the 1st one, the average
total delay will be 0.5 + (N-1); the average variance of the delay will
be 1/4; the standard deviation will be 1/2.

That is, a sum of multiple random picks does indeed result in more
randomization than a single random pick. 

-- Christian Huitema