Find the variance of the number of islands occupied.
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.