=+7. Suppose Q(s) is a generating function with mean and variance 2. If 1 is small and positive, then verify that Q(s)

=+7. Suppose Q(s) is a generating function with mean μ and variance σ2.

If μ − 1 is small and positive, then verify that Q(s) has approximate extinction probability e−2(μ−1)/σ2

. Show that this approximation equals 0.892 for Lotka’s demographic data. (Hints: Put t = ln s and L(t) = ln Q(s). Expand L(t) in a second-order Taylor series around t = 0.)