Please help to solve the task (especially the bolded part): 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:
Please help to solve the task (especially the bolded part):
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
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.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
