Problem 1.73 A laboratory keeps a population of aphids. The probability of an aphid passing a day uneventfully is q< 1. Given that a day is not uneventful, there is a probability r that the aphid will have one offspring, a probability s that it will have two offspring, and a probability t that it will die of exhaustion, where r+s+t=1. Offspring are ready to reproduce the next day. The fates of different aphids are independent, as are the events of different days. The laboratory starts out with one aphid. Let X, be the number of aphids at the end of n days. Show how to obtain an expression for the PGF ,(z) of X„. What is the expected value of X,? Show that the probability of extinction does not depend on q and that if 2r + 3s

Problem 1.73 A laboratory keeps a population of aphids. The probability of an aphid passing a day uneventfully is q< 1. Given that a day is not uneventful, there is a probability r that the aphid will have one offspring, a probability s that it will have two offspring, and a probability t that it will die of exhaustion, where r+s+t=1. Offspring are ready to reproduce the next day. The fates of different aphids are independent, as are the events of different days. The laboratory starts out with one aphid. Let X, be the number of aphids at the end of n days. Show how to obtain an expression for the PGF ,(z) of X„. What is the expected value of X,? Show that the probability of extinction does not depend on q and that if 2r + 3s

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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