Consider the following branching process Xn. Generation 0 has 1 individual, i.e. X0 = 1. Then, each individual of each generation, independently of al

Consider the following branching process Xn. Generation 0 has 1 individual, i.e. X0 = 1. Then, each individual of each generation, independently of all other individuals, gives at most 2 descendants and immediately dies. Let p ? [0,1] be the probability an individual does not give any descendants and let q ? [0,1] be the probability the individual gives 2 descendants. Of course, p + q ? 1 (why?).(a) What is the condition on p and q for this process to have a chance at survival?(b) Compute the probability of survival. (Hint: probability-generating function.)

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