A07.3 Challenge A viral meme starts in one account, and is re-shared by K other accounts, where K is a non-negative discrete random variable. Assume that the future behaviour following from each of the initial re-shares is independent and distributed identically to the sharing behaviour from the initial creation: after k initial re-shares we have k independent and identically distributed copies of the initial meme process. Let d be the probability that the meme eventually dies out, which is also the probability that any of the k sub-branches of the process dies out. Use the law of total probability to justify why d = X∞o k=0 P (K = k) d k = Ed K. Suppose

A07.3 Challenge A viral meme starts in one account, and is re-shared by K other accounts, where K is a non-negative discrete random variable. Assume that the future behaviour following from each of the initial re-shares is independent and distributed identically to the sharing behaviour from the initial creation: after k initial re-shares we have k independent and identically distributed copies of the initial meme process. Let d be the probability that the meme eventually dies out, which is also the probability that any of the k sub-branches of the process dies out. Use the law of total probability to justify why d = X∞o k=0 P (K = k) d k = Ed K. Suppose

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.3: Binomial Probability

Problem 33E: Sick leave probability that a given worker at Dyno Nutrition Will call in sick on a Monday is 004....

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