A type of network router has a bandwidth total to first hardware failure called ? expressed in terabytes. The random variable ? is modeled by a distribution whose density is given by one of the following functions:fs(s) = 1/? for s [0,?]with a single parameter ?. Consider the bandwidth total to failure ? of the sequence of the two routers of the same type (one being brought up automatically when the first is broken).Express ? in terms of the bandwidth total to failure of single routers ?1 and ?2. Formulate realistic assumptions about these random variables. Calculate the density function of the variable ?. Given an experiment with the dual-router-system yielding a sample ?1 , ?2 , ..., ?? , calculate the likelihood function for ?. Propose a transformation of this likelihood function whose maximum is the same and can be computed easily.An actual experiment is performed, the infrastructure team has obtained the bandwidth totals to failure given by the sequence ?10 of numbers (225, 22, 18, 93, 61). Estimate the model-parameter with the maximum likelihood and compute the expectation of the bandwidth total to failure of the dual-router-system. A type of network router has a bandwidth total to first hardware failure called S expressed in terabytes.The random variable S is modeled by a distribution whose density is given by one of the followingfunctions:f(s)=Өfor s € [0, 0]SEwith a single parameter 8. Consider the bandwidth total to failure T of the sequence of the two routers ofthe same type (one being brought up automatically when the first is broken).Express T in terms of the bandwidth total to failure of single routers S1 and S2. Formulate realisticassumptions about these random variables. Calculate the density function of the variable T. Given anexperiment with the dual-router-system yielding a sample T₁, T2, ..., Tn, calculate the likelihood functionfor 8. Propose a transformation of this likelihood function whose maximum is the same and can becomputed easily.An actual experiment is performed, the infrastructure team has obtained the bandwidth totals to failuregiven by the sequence $10 of numbers (225, 22, 18, 93, 61). Estimate the model-parameter with themaximum likelihood and compute the expectation of the bandwidth total to failure of thedual-router-system.

Answered: A type of network router has a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A type of network router has a bandwidth total to first hardware failure called ? expressed in terabytes. The random variable ? is modeled by a distribution whose density is given by one of the following functions:

fs(s) = 1/? for s [0,?]

with a single parameter ?. Consider the bandwidth total to failure ? of the sequence of the two routers of the same type (one being brought up automatically when the first is broken).
Express ? in terms of the bandwidth total to failure of single routers ?1 and ?2. Formulate realistic assumptions about these random variables. Calculate the density function of the variable ?. Given an experiment with the dual-router-system yielding a sample ?1 , ?2 , ..., ?? , calculate the likelihood function for ?. Propose a transformation of this likelihood function whose maximum is the same and can be computed easily.

An actual experiment is performed, the infrastructure team has obtained the bandwidth totals to failure given by the sequence ?10 of numbers (225, 22, 18, 93, 61). Estimate the model-parameter with the maximum likelihood and compute the expectation of the bandwidth total to failure of the dual-router-system.