Sketch the probability distribution for each set of islands. Why does the second set fail to follow the binomial distribution?
Consider two sets of ten islands. In the first set, each island has a 0.2 chance of switching from empty to occupied, and a 0.1 chance of switching from occupied to empty. The equilibrium fraction occupied is 2/3. In the second set of ten islands, all are occupied if the weather is good (probability 2/3) and all empty if the weather is bad (probability 1/3). Compute the following for both sets of islands.