2. (10 pts) CT FS properties. If x4[n] is the same as x3[n], but shifted to the right by 1, then what are the spectral coefficients of x4[n]? Hint: text, page 221.
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2. (10 pts) CT FS properties. If x4[n] is the same as x3[n], but shifted to...
3. (5 pts) CT FS properties. Observe that x1[n] is odd, what are the properties of the spectrum coefficients (mag and phase)? Observe that x3[n] is even, what are the properties of the spectrum coefficients (mag and phase)?
1. (45 pts) DT FS. Find the fundamental period and the Fourier Series (FS) spectral coefficients for these periodic signals. Sketch the spectrum in magnitude and phase. Express each x[n] as the sum of the spectral coefficients for k = [0, N-1]. a. ?1[?] = ???( ? 3 ?) b. ?2 [?] = cos ( ? 3 ?) + sin( ? 4 ?) c. ?3[?]
Run the following multivariate linear regression models:
Model 1: X3 and X4
Model 2: X2,X3,and X4Model 3: X1, X3 and
X4Discuss the correlation
between each two variables using adjusted R2 and P-value. Write the
estimated equation of Y for each regression model. Briefly comment
of the Residual Plots.
SUMMARY OUTPUT Regression Statistics Tourist arrivals (X3) Residual Plot Mu R Square Adjusted R Square Standard Error Observations 0.77706686 0.60383291 0.58622549 26011267.3 48 ANOVA Significance F 4.6406E 16 2.3203E 16 34.2942181 8.9591E-10...
Amplitude=3; fs=8000; n=0:399; t=0:1/fs: n*1/fs-1/fs; signal=3+3*cos(2*pi*1100*t)+3*cos(2*pi*2200*t)+3*cos(2*pi*3300*t); fftSignal= fft(signal); fftSignal=f ftshift (fftSignal); f=fs/2*linspace(-1,1,fs); plot(f,abs(fftsignal); xlabel('Frequency(Hz)’) ylabel('amplitude(v)') title('Spectral domain') plz code above using For ..End loop to archive the same results.
(20 pts) Suppose that 1, 2, X3, X4 are independent random variables, all of which have mean μ and variance σ2 (a) Yi = 0.25x1 + 0.25x2+ 0.25x3 + 0.25x4 (b) ½ = 0.1X1 + 0.2X2 + 0.3X3 + 0.4X4 (c) YS = 0.5X1 + 0.4X2 + 0.3X3-0.2X1 What do you observe about the expectation of Y ,½,⅓? Which of these random variables has the LEAST variance?
Problem 2. This is adapted from our textbook. Let X -[x1,x2, x3,x4 be a set of four monetary prizes, where 0 < x1 < x2 < 13 < x4. Stowell claims he is an expected utility maximizer. He is observed to choose the lottery π-(1, 1, 1, ) over the lottery π,-(0Ί, , Ỉ ). Based 1 11 7 4 24 24) Based on that observation, can you conclude that he is truly an expected utility maximizer, as he [10...
Please send the detail solution ASAP
Assume X = [X1, X2, X3, X4]T ~ N(µ, C). Consider [1 2 2 6 7 8. µ = E[X] C= 3 7 11 12 4 8 12 16 o What is the pdf of px,(x) ? o What is the pdf of px1,X3(x1, 13) ? O Determine E[X2] ? O Determine E[X2 + X3] ? O Determine E[(X2 – X2)²] ? O Determine E[(X2 – X2)(X3 – X3)] ? O Determine E[X2X3] ?
Find the DTFT a. x1[n]=(.3)^nµ[n] b. x2[n]=(.3)µ[n-1] c. x3[n]=(.3)^n(µ[n]-µ[n-10]) d. x4[n]=(.3)^n(µ[n-1]-µ[n-10]) e. x5[n]=δ[n] f. x6[n]=δ[n-1] g. x7[n]=δ[n]+3δ[n-1]+7δ[n-3]
Question 4 (a) Find the DFT of the series x[n)-(0.2,1,1,0.2), and sketch the magnitude of the resulting spectral components [10 marks] (b) For a discrete impulse response, h[n], that is symmetric about the origin, the spectral coefficients of the signal, H(k), can be obtained by use of the DFT He- H(k)- H-(N-1)/2 Conversely, if the spectral coefficients, H(k), are known (and are even and symmetrical about k-0), the original signal, h[n], can be reconstituted using the inverse DFT 1 (N-D/2...
2. Let Xi, X2, X3, X4,X5 be a random sample of size 5 from a popula- tion following the standard normal distribution (mean 0 and variance 1), and let X Σ5 i Xi/5. Let 6 be another independent observation from the same popula- tion. What is the distribution of (b) Z-Σ51 (Xi-X)2, Why?