Problem: Estimate the probability that a message can pass through a network of switches and communication links, by testing only switches and links.



Population 1: 



Population 2: 

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?

General SetupOutlineIntroduction