Problem: Estimate the probability that a message can pass through
a network of switches and communication links, by testing only switches
The message can be delivered whenever there is a fault-free path connecting
left to right, assuming that the links going into the first and out of
the last switches are working. So we have:
P[transmission] = p13p22 [
2 + 2p1p2 - 5p1p22
+ 2p1p23 ]
We assume that we will be allowed a fixed number N of observations
of the two populations.
Question: How should one sample from the two populations, to obtain the
best estimate of the message transmission probability?