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\fConsider the signal f[k], with k = 1, ..., N, and signal model Va,be [k] = asin(wok) + bcos(wok) + c with a, b, and c constants to be determined and all = . Consider the function for the least squares criterion (same as the problem above). Part A: (written) Write the function for the sum of the squares of the residual errors between the signal f [k] and the Va,b,c [k] calculated with the signal model. Part B: (written) Write the solution for the minimum of the function in part A with respect to the parameters a, b, and c. (Hint: you should end up with a linear system of equations for unknowns a, b, and c).Problem 3: Least squares I (WRITTEN & MATLAB) Consider the signal f[k], with k = 1, .. N, and a linear signal model Vab [k] = ak + b with a and b constants to be determined. Consider the function for the sum of the squares of the residual errors between the signal f[k] and the Va,s [k] calculated with the linear signal model: Q(a, b) = (ak + b- f[kj)? Part A: (WRITTEN) Write the solution for the minimum of the function above with respect to the parameters a and b. (Hint: you should end up with a linear system of equations for unknowns a and b which can be written in matrix form and solved in MATLAB) Part B: (MATLAB) Using the least squares formulation you derived in part A, Write a MATLAB script to compute the least squares fit of the model to the signal f(given below). Calculate the constants a and b for the linear signal model. Plot the raw signal as well as the best fit found (overlaid on top of each other), and give the model parameters for a and b. (Note: display the output of a and b by not suppressing the line solving for it with a semicolon) f =[0 2 1 2 3 3 4 7 7 9 11 11]Problem 2 (10 points) Consider a non-uniform random variable X with M = 8 possible outcomes and probabilities (1/2, 1/4, 1/8, 1/16, 1/64, 1/64, 1/64, 1/64). We use one symbol to represent one outcome, so we have 8 types of symbols (A, B. C, D. E, F. G. H). Then we transmit 1024 symbols from point s to point d. In this 1024- symbol sequence, it turns out that the numbers of these & type symbols are (516, 255, 126, 68, 17, 18, 10, 14), respectively (a) Compute the entropy H(X) in bits. (b) Consider a coding scheme cy, A + 000, B + 001, C + 010, D + 011, E - 100, F - 101, G - 110, H - 111, to transmit these 1024 symbols. Compute the total bits using scheme c. (c) Similarly, consider another coding scheme ca, A + 0, B - 10, C - 110, D + 1110, E - 11110, F - 111110, G - 1111110, # + 11111110, to transmit these 1024 symbols. Compute the total bits using scheme ca. On average, how many bits are used to transmit one symbol in this transmitted sequence?\fSuppose Y and X are two binary random variables. Consider fitting a linear regression: Y = Bole + Bulls X + cals. Show that Bols = P(Y = 1 X = 1) - P(Y = 1/X = 0).Problem 8. Multivariable linear regression analysis In this problem, we consider the linear regression analysis of two independent variables (two input variables). In the class example, we have considered the problem of regressing a set of data of house price as a function of the house area footage. The following set of data points records the house price as a function of the house area and lot size. House Area (ft2) Lot Size (ft2) House Price (US$) 1474 10000 150000 1560 9500 145000 1584 12000 160000 1645 13000 170000 1712 13500 190000 1870 13000 200000 Employ the following linear regression model: y = f(X1,X2) = do + di*1 + 012X2 where, x, and X2 denote the variables of house area and lot size, respectively. a) Employing the principle of least squares minimization, derive the linear regression equation to determine the unknown parameters do, 11, d12. You may scan your handwritten derivation and include in the homework file. b) Predict the value of a house with area of 1,474 ft and lot size of 12,000 ft?. function r2 = CoeffDeter(fitted_fun,x_data,y_data) 9%% Calculations Sr = sum((y_data-fitted_fun(x_data)).^2); % Total error between data points 9% and fitting model St = sum((y_data-mean(y_data)).^2); % total statistical error 12 =1 - Sr/St; end