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  3. problem 2 problem 1 doesnt need to be done its...

Question: problem 2 problem 1 doesnt need to be done its...

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166 Branching processes is a branching process whose .... is a branchin the result zes have mean μ (s l ) and variance σ 2, then var( ZnJun of Problem 9.6.1 to show that, if Zo. z 2. Use ditioning on the value of Zm, show th ose fa outition theorem and conditioning on the value of Z9.6 Problems I. Let X1 , X2. . . . be independent random variables, each with mean μ and variance σ2, and let N be a random variable which takes values in the positive integers (1,2, ..) and which is independent of the Xi. Show that the summ has variance given by If Zo. Z mean 11 and variance ơ2, use the above fact to show that 1. . .. are the generatio n sizes of a branching process in which each family size has var(Zn) σ 2/1n -1 + 112 var(Zn-1), Deduce an expression for var(Zn) in terms of μ, σ 2, and n.

Problem 2. Problem 1 doesn't need to be done, it's here for reference

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