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
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 21 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON