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1) Determine the autocorrelation function RXX(T) for the continuous-time random process X(t) that has the power spectrum (show all steps for your derivation)
where K > 0 is a real constant and WX is the spectral extent of the process.
2) Write a Matlab code to produce the estimated power spectrum from the autocorrelation function obtained in step (1) for N=5 normalized frequencies. Note: You may use the FFT function to calculate the Fourier transform. See Example 7.5-5
3) Plot on the same figure the estimated power spectrum on top of the given power spectrum
4) Repeat steps (2) and (3) for N=10 normalized frequencies.
5) Plot on the same figure the estimated power spectrum of step (4) on top of the given power spectrum
6) Compare your results
Given a graph, an independent set, is a collection of nodes which have no edges among them. Thus, in the following graph,the nodes B, D, and E form an independent set because there are no edges connecting one of them to the other two.
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a. Derive the concentration profile of pyruvate in the film.
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Compare the results of i) to the exact solution and comment on the accuracy of the numerical algorithm and adopted step size.
Looking back at the data examples you have provided in the previous discussion questions on this issue, how might adding confidence intervals help managers accept the results better? Why?
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What is the probability that my right headlight will last for at least 1900 hours given that it has not failed after 950 hours?
How can you or your department decide whether or not the observed differences over time are important? How could using a mean difference test help?
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