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Problem 1 Suppose Yt = St + Nt; t E R where (St; t e R} and (It/t; l E R} are zero mean WSS and orthogonal. Suppose that we wish to mintage the proccaa X, - f 1.(t - r).9,4r. t E It with an tatimate of the ham oo = 7 h(t - r)lcdr. f 12. where k and h are impulse responses of linear-time invariant systems. -oo Show that:
12{(X, - it)] = EIK(w) - Hhell2Ss(w)+ ill(w)17S,v(w)f
where K and H are the transfer function of k and h, nespetilvely, and Sc and SN are the power spectral densities of (St; I E R) and (Ns; t E R), respectively.
Problem 2 Let (X,; I E 12) be a continuous time, zero mean Gaussian random proem with spectral density Sx (co) = Vw E R. Lot HP) and CP) be the transfer functions of the two linear systems (time-invariant) with impulse responses h(t) and g(t), respectively. The proems (X1) is passed through the filter h(t) to obtain (Vi; t e RI and it is also passed through the filter g(t) to obtain (V,; t c a) Find &w(t. s) b) Under what assumptions Vs and Vt are independent ?
A bag contains 10 balls numbered from 0 to 9. the balls are such that the person picking a ball out of the bag is equally likely to pick anyone of them. A person picked a ball and replaced it in the bag after noting its number. He repeated this proce..
Discuss when it is appropriate to use the t-based confidence interval for m. Using Table A.4 (page 792), find t.100, t.025, and t.001 based on 11 degrees of freedom. Also, find these t points based on 6 degrees of freedom.
For each of the following situations, find the mean, variance, and standard deviation of the sampling distribution of the sample mean x:
Analysis ToolPak or the StatPlus:mac LE software function descriptive statistics, generate and show the descriptive statistics for each appropriate variable in the sample data set
In a sample of 30 students of the Academy, we obtained the following data which represents the weights of these students 65, 59, 47, 67, 56, 50, 74, 45, 83, 72, 71, 53, 82, 58, 64 79, 55, 88, 56, 69, 50, 68, 66, 62, 59, 52, 72, 63, 56, 91 Answer the ..
A doctor claims that the standard deviation of systolic blood pressure is 12 mmHg. A random sample of 24 patients found a standard deviation of 14 mmHg. Assume the variable is normally distributed.At a = 0.01, what are the critical X²
What proportion of the 400 salespeople received a bonus last year? What proportion of the 400 salespeople attended the special sales training program at the beginning of last year?
Suppose the bulb factory will operate only 4 hours. What is the pdf of the number of defective bulbs in 4 hours of works? Calculate the variance of the number of defective bulbs. What is the probability to have no defective bulb during 4 hours of ..
The level of calcium in the blood in healthy young adults varies with mean about u = 9.50 milligrams per deciliter and standard deviation about .40 milligram per deciliter. A clinic in rural Guatemala measures the blood calcium level of 64 healthy pr..
A study of college football games shows that the number of holding penalties assessed has a mean of 2.3 penalties per game and a standard deviation of penalties per 1.1 game. What is the probability that, for a sample of 40 college games to be played..
Flybynight Airlines measured their numbers of lost bags in one month and found that they had lost 130 bags for 10,000 customers. If the average number of bags per customer is 1.3, how many errors per million opportunities (epmo) does this represent?
A local ice-cream store receives an average of 3 customers per hour. Assume that the arrival events are well described by Poisson distribution. The cashier wants to leave the store to run an errand. The manager computes the expected time T between..
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