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A type of network router has a bandwidth total to first hardware failure called S expressed in terabytes. The random variable S is modelled by an exponential distribution whose density is given by: s(t) with a single parameter 0. Consider the bandwidth total to failure T of the sequence of the two routers of the 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 S, and S2. Formulate realistic assumptions about these random variables. Calculate the density function of the variable T.

A type of network router has a bandwidth total to first hardware failure called S expressed in terabytes. The random variable S is modelled by an exponential distribution whose density is given by: s(t) with a single parameter 0. Consider the bandwidth total to failure T of the sequence of the two routers of the 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 S, and S2. Formulate realistic assumptions about these random variables. Calculate the density function of the variable T.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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A type of network router has a bandwidth total to first hardware failure called S expressed in terabytes. The random variable S is modelled by an exponential distribution whose density is given by: s(t) with a single parameter 0. Consider the bandwidth total to failure T of the sequence of the two routers of the 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 S, and S2. Formulate realistic assumptions about these random variables. Calculate the density function of the variable T. Given an experiment with the dual-router-system yielding a sample T,, T2, -, Tn, calculate the likelihood function for 0. 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 following bandwidth total to failures: 9.2, 5.6, 18.4, 12.1, 10.7 Estimate the model-parameter with the maximum likelihood and compute the expectation of the bandwidth total to failure of the dual-router-system.
Transcribed Image Text:A type of network router has a bandwidth total to first hardware failure called S expressed in terabytes. The random variable S is modelled by an exponential distribution whose density is given by: s(t) with a single parameter 0. Consider the bandwidth total to failure T of the sequence of the two routers of the 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 S, and S2. Formulate realistic assumptions about these random variables. Calculate the density function of the variable T. Given an experiment with the dual-router-system yielding a sample T,, T2, -, Tn, calculate the likelihood function for 0. 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 following bandwidth total to failures: 9.2, 5.6, 18.4, 12.1, 10.7 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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Can you please follow up on the question and answer the second part: 'Propose a transformation of this likelihood function whose maximum is the same and can be computed easily'

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