1. Let T be the minimal value of n such that Xn = 0. It iscalled the extinction time. If the process survives, we setT = ∞. Find P (T= 2 | ZO = 1).Lambda = 0.1968, the process will go extinct.2. Find P (T>2|Z0 = 1), where T is the extinction time.Consider the complement of the event {T > 2}3.For n > 1, let fn = P(T > 10|Z₁ = n). Express fa in terms of fi.Hint: Offspring of 10 individuals in generation zero form 10 independent branching processes.Survival of the whole process is equivalent to the survival of at least one of these 10 sub-processes.

This question deals with the probability of the extinction time of an exponentially distributed…

Answered: 1. Let T be the minimal value of n such…

MATLAB: An Introduction with Applications

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1. Let T be the minimal value of n such that X₁ = 0. It is called the extinction time. If the process survives, we set T = ∞. Find P (T=2 | ZO = 1). Lambda= 0.1968, the process will go extinct. 2. Find P (T> 2|20 = 1), where T is the extinction time. Consider the complement of the event {T > 2)