A type of network router has a bandwidth total to first hardware failure called expressed in terabytes. The random variable is modelled by an exponential distribution whose density is given by: () = 1 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 following bandwidth totals to failure: 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.