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 a distribution whose density is given by one of the following functions:
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 a distribution whose density is given by one of the following functions:
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
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![Task 3: Transformed Random Variables
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 a distribution whose density is given by one of the following functions:
• (if 9 = 0): f(s) = e
• (if 9 = 1): fs(s)
. (if 9 = 2): fs(s) : =
ste
for s € [0,0]
2495
with a single parameter 8. 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 S₁ 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 T₁, T2, ..., T, calculate the likelihood
function for 8. 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 bandwidth totals to failure given by
the sequence $10 of numbers. Estimate the model-parameter with the maximum likelihood and compute the
expectation of the bandwidth total to failure of the dual-router-system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a5e1a3a-5891-4b70-8a81-26bf407fd11c%2F1d6ec6e2-719d-4c03-be8b-dbd8a64bdac2%2Fdb9rclo_processed.png&w=3840&q=75)
Transcribed Image Text:Task 3: Transformed Random Variables
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 a distribution whose density is given by one of the following functions:
• (if 9 = 0): f(s) = e
• (if 9 = 1): fs(s)
. (if 9 = 2): fs(s) : =
ste
for s € [0,0]
2495
with a single parameter 8. 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 S₁ 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 T₁, T2, ..., T, calculate the likelihood
function for 8. 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 bandwidth totals to failure given by
the sequence $10 of numbers. 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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