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Exercise 5-6.2 Show that the estimate of the variance given by equation (5-1 4) is an unbiased estimate. That is, E[&,i] = a,i
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Exercise 5-6.1 Using a random number generator obtain 1 00 random numbers uniformly distributed between O and 1 0. Using numerical methods a) estimate the mean b) estimate the variance of the process c) estimate the standard deviation of the estimate...
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Exercise 5-5.2 A random process has sample functions of the form X(t) = A cos (wt+ fJ) where A is a random variable having a magnitude of + 1 or -1 with equal probability and e is a random variable uniformly distributed between O and 21l' . a) Is X(t...
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Exercise 5-5.2 A random process has sample functions of the form X(t) = A cos (wt+ fJ) where A is a random variable having a magnitude of + 1 or -1 with equal probability and e is a random variable uniformly distributed between O and 21l' . a) Is X(t...
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Exercise 5-4.2 A random process is described by X(t) = A+ B cos (wt+ 8) where A is a random variable that is uniformly distributed between -3 and +3, B is a random variable with zero mean and variance of 4, w is a constant, and 8 is a random variable...
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Exercise 5-4.1 a) For the random process described in Exercise 5-3.2, find the mean value of the random variable X(t1/4). b) Find the mean value of the random variable X(3t1/4) . c) Is the process stationary? Why?
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Exercise 5-3.2 A random process has sample functions of the form 00 X(t) = L Anf(t -nt1 ) n=-oo where the An are independent random variables that are uniformly distributed from 0 to 1 0, and f (t) = 1 0 :::: t :::: (1/2)t1 = 0 elsewhere a) Is this p...
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Exercise 5-3.1 A sample function of the random process described by equation (5-3) is observed to have the following values: X(1 ) = 1 .21 306 and X(2) = 0.73576. a) Find the values of A and {3 . b) Find the value X(3.21 89).