Let X 0 1, and S t 0 X t , the total number of all particles in all generations Show that E S , if 1 and E S 1 (1), if 1 If f 0 3 4, and f 2 1 4, what is the total mean number of the particles

Question: Let X 0 = 1, and S = t=0 X t , the total number of all particles in all generations. Show that

Let X₀ = 1, and S = Σ^∞_t=0 X_t , the total number of all “particles” in all generations. Show that E{S} = ∞, if μ ≥ 1; and E{S} = 1/(1−μ), if μ< 1. If f₀ = 3/4, and f₂ = 1/4, what is the total mean number of the particles?

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