Ri = 4 with probability 0.5, Ri = 0.25 with probability 0.5. Find the approximate normal distribution for ln(P50), the log of the population size after 50 time steps.
Although the Central Limit Theorem applies to the sums of independent and identically distributed random variables, we can use logarithms to analyze products of independent and identically distributed random variables. Consider populations growing for the given number of years with the given distribution for the random variable R giving per capita production. Find the normal distribution that approximates the logarithm of the population size P, assuming that P0 = 100.