A type of network router has a bandwidth total to first hardware failure called ? expressed in terabytes. The random variable ? is modelled by a distribution whose density is given by ?(?) = 1/θ for s ∈ [0, θ].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 and calculate the density function of the variable T.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, and the infrastructure team has obtained the bandwidth totals to failure given by the sequence [35, 19, 9, 18, 25]. Estimate the model-parameter with the maximum likelihood and compute the expectation of the bandwidth total to failure of the dual-router-system.

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Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

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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 modelled by a distribution whose density is given by ?(?) = 1/θ for s ∈ [0, θ].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 and calculate the density function of the variable T.
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, and the infrastructure team has obtained the bandwidth totals to failure given by the sequence [35, 19, 9, 18, 25]. Estimate the model-parameter with the maximum likelihood and compute the expectation of the bandwidth total to failure of the dual-router-system.

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