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1/4 2. The Sneaky Tricks software virus infects networked computers according to a branching process, with daily infection size distribution Y Binomial (2, 0.7). Assume that the virus is cleared from the original host computer at the end of the day. ~ (a) Working directly from the probability function, show that the PGF of Y is G(s) = (0.7s +0.3)2 for s € R. (b) Find the probability that the number of infected computers will eventually fall to zero, starting from a single infected host computer. (c) Suppose there are 8 infected computers at generation (day) 10. What is the proba- bility that the network becomes infection free?

1/4 2. The Sneaky Tricks software virus infects networked computers according to a branching process, with daily infection size distribution Y Binomial (2, 0.7). Assume that the virus is cleared from the original host computer at the end of the day. ~ (a) Working directly from the probability function, show that the PGF of Y is G(s) = (0.7s +0.3)2 for s € R. (b) Find the probability that the number of infected computers will eventually fall to zero, starting from a single infected host computer. (c) Suppose there are 8 infected computers at generation (day) 10. What is the proba- bility that the network becomes infection free?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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2. The Sneaky Tricks software virus infects networked computers according to a branching process, with daily infection size distribution Y Binomial (2, 0.7). Assume that the virus is cleared from the original host computer at the end of the day. ~ (a) Working directly from the probability function, show that the PGF of Y is G(s) = (0.7s +0.3)2 for s € R. (b) Find the probability that the number of infected computers will eventually fall to zero, starting from a single infected host computer. (c) Suppose there are 8 infected computers at generation (day) 10. What is the proba- bility that the network becomes infection free?
Transcribed Image Text:2. The Sneaky Tricks software virus infects networked computers according to a branching process, with daily infection size distribution Y Binomial (2, 0.7). Assume that the virus is cleared from the original host computer at the end of the day. ~ (a) Working directly from the probability function, show that the PGF of Y is G(s) = (0.7s +0.3)2 for s € R. (b) Find the probability that the number of infected computers will eventually fall to zero, starting from a single infected host computer. (c) Suppose there are 8 infected computers at generation (day) 10. What is the proba- bility that the network becomes infection free?
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