A chain letter e-mail asks its reader to forward it to 12 other people. 92% of the people delete the letter without forwarding it; however, 8% do forward it to 12 other people. (a) Model the scenario with a branching process. What is the expectation of the offspring distribution? Is the process subcritical, critical or supercritical? (b) What is the probability that the chain letter will stop spreading eventually? (c) Assuming that the creator of the chain letter sent it to 12 other people, what is the expected number of e-mails sent throughout the entire `` lifetime '' of the chain letter?
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