Consider a branching process with generation sizes Zn satisfying Zo = 1 and P(Z₁ = 0) = 0.Pick two individuals at random (with replacement) from the nth generation and let L be the index ofthe generation which contains their most recent common ancestor. Show that P(L = r) = E(Z¹) -E(Z1) for 0 ≤r 0?

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Answered: Consider a branching process with…

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...

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Suppose we toss m (numbered) balls into n (numbered) bins randomly.Let X be the number of empty bins.In class we showed that E(X) = n(1 − 1/n)^m. For n = 10 and m = 5, 10, 20 calculate E(X).For the case n = 10 and m = 20, interpret the result for E(X) (write one sentence in English to explain what the result means).
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Old Faithful is a geyser located in Yellowstone National Park in Wyoming, USA. Millions of travelers come from afar to witness Old Faithful's eruptions each year. The data provided show the waiting time until the next eruption for 272272 Old Faithful eruptions in 1990. Suppose that prior to 1990, travelers to Yellowstone are told that Old Faithful is expected to erupt, on average, every 6969 minutes, and park scientists believe that this average is no longer true. Suppose that, based on historical data available over several decades, the scientists are comfortable assuming that all eruption waiting times have a known standard deviation of 17.24817.248 minutes. 54 74 62 85 55 88 85 51 85 54 84 78 47 83 52 62 84 52 79 51 47 78 69 74 83 55 76 78 79 73 77 66 80 74 52 48 80 59 90 80 58 84 58 73 83 64 53 82 59 75 90 54 80 54 83 71 64 77 81 59 84 48 82 60…

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