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Repeat construction of the optimal ?lter from Example 7.3.1 in the case when the useful signal Y (t)has a more general power spectrum a SY (f ) = b2 + f 2 , and the uncorrelated white noise N(t) has arbitrary power spectrum SN (f ) ≡ N . Discuss the properties of this ?lter when the noise power is much bigger than the power of the useful signal, that is, when N » SY (f ). Construct the optimal acausal ?lters for other selected spectra of Y (t) and N(t).
write the Data Analysis section of the methods and the Results for an experiment, as if for publication in a journal. The experiment and results are completely fabricated an
When the experiment is performed many times, the chain ends in state one approximately 20 percent of the time and in state two approximately 80 percent of the time. Compute
Write a computer program to simulate the queue in Exercise 20. Have your program keep track of the proportion of the time that the queue length is j for j = 0, 1, . . . , n
Let Sn denote the total of the outcomes through the nth toss. Show that there is a limiting value for the proportion of the first n values of Sn that are divisible by 7, and c
Using the result of Exercise 17, calculate the expected to reach snake eyes, in equilibrium, and see if this resolves the apparent paradox. If you are still in doubt, simula
Let P be the transition matrix of an ergodic Markov chain and P∗ the reverse transition matrix. Show that they have the same fixed probability vector w.
Modify the program ErgodicChain so that you can compute the basic quan- tities for the queueing example of Exercise 11.3.20. Interpret the mean recur- rence time for state 0
Estimate the expected number of sites occupied for a given value of p. If p is small, can you choose the tape long enough so that there is a small probability that a new job
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