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.

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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Question

I need the answer as soon as possible

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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