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![Answers Given that table x 012 3 15. I 9=f(1) 12 14 15.]. f(3) =2 f.cx) = f (2) + f(3) = f(2) (-2) 3-2 = !!. t .(-4-10) (0-2)](http://img.homeworklib.com/questions/dfc84ac0-d59f-11ea-8375-7b1e168325b6.png?x-oss-process=image/resize,w_560)
Exercise 6: Given the table of the function f(x)-2" 2 X 0 3 2 f(x) 1 2 4 8 a) Write down the Newton polynomial...
Exercise 6: Given the table of the function f(x)-2" 2 X 0 3 2 f(x) 1 2 4 8 a) Write down the Newton polynomials P1(x), P2(x), Pa(x). b) Evaluate f(2.5) by using Pa(x). c) Obtain a bound for the errors E1(x), E2(x), Es(x) Exercise 7: Consider f(x)- In(x) use the following formula to answer the given questions '(x) +16-30f+16f,- 12h a) Derive the numerical differentiation formula using Taylor Series and find the truncation error b) Approximate f'(1.2) with h-0.05...
(3.2) Consider the data given in the following table 05 1 15 f(x) 0 2 0 6 1 2 20 (4) (a) Approximate f with a functi...
(3.2) Consider the data given in the following table 05 1 15 f(x) 0 2 0 6 1 2 20 (4) (a) Approximate f with a function of the form q (x) = kxm (4) (b) Approximate f with a function of the form g2(x) = be Which approximation between q and g2 1s more appropriate for the given data? Justify your (3) (c) answer < In, and a piecewise cubic polynomial Consider a set of points (I,) Such that...
Consider the following data table: 0 2i = 0.2 0.4 f(xi) = 2 2.018 2.104 2.306...
Consider the following data table: 0 2i = 0.2 0.4 f(xi) = 2 2.018 2.104 2.306 0.6 0.2 and 23=0.4 is The linear Lagrange interpolator L1,1 (2) used to linearly interpolate between data points 12 (Chop after 2 decimal places) None of the above. -2.50x+0.20 -5.00x+2.00 -5.00x+2.00 5.00x-1.00 Consider the following data table: 2 Ti = 0 0.2 0.4 0.6 f(x) = 2.018 2.104 2.306 0.2 and 23 = 0.4, the value obtained at 2=0.3 is Using Lagrange linear interpolation...
You are given the table below. 16 20 4 8 12 X f(x) 12 2417 6...
You are given the table below. 16 20 4 8 12 X f(x) 12 2417 6 30 Use the table and n = 4 to estimate the following. Because the data is not monotone (only increasing or only decreasing), you should sketch a possible graph and draw the rectangles to ensure you are using the appropriate values for a lower estimate and an upper estimate. 20 f(x)dx lower estimate upper estimate Estimate the area of the region under the curve...
The following y vs. x data is given x y 1 2.25|3.7 15.1 4.256 13.7 15.1...
The following y vs. x data is given x y 1 2.25|3.7 15.1 4.256 13.7 15.1 The data is fit by a quadratic spline given by ( 2.85 + 1.4x, 1< x < 2.25 f(x) = { cx? + dx +e, 2.25 < x < 3.7 (fx2 + gx + h, 3.7 < x < 5.1 The value of d most nearly is
FITTING A QUADRATIC PARABOLA 8-11 Fit a parabola (7) to the points (x, y). Using MATLAB...
FITTING A QUADRATIC PARABOLA 8-11 Fit a parabola (7) to the points (x, y). Using MATLAB 10. hr] Worker's time on duty, y [sec] = His/her reaction time, (t, y) (1, 2.0), (2, 1.78), (3,1.90), (4, 2.35), (5, 2.70)
FITTING A QUADRATIC PARABOLA 8-11 Fit a parabola (7) to the points (x, y). Using MATLAB 10. hr] Worker's time on duty, y [sec] = His/her reaction time, (t, y) (1, 2.0), (2, 1.78), (3,1.90), (4, 2.35), (5, 2.70)
Assuming that the first spline is linear in quadratic spline interpolation, the number of unknowns in...
Assuming that the first spline is linear in quadratic spline interpolation, the number of unknowns in the splines for 10 data points is QUESTION 2 The following y vs. x data is given 1 225 3.7 5.1 4.25 68615.1 The data is fit by quadratic spline interpolants given by AX) - 2.85 +1.4x, 1 5X5 2.25 AXX2dx +2.25 SX5 3.7 A x) = fx2gx+, 3.7<*5.1 The value of d most nearly is QUESTION 3 The following y vs. x data...
Consider the data: X- 1 Y- 6 3 14 5 7 2 20 9 11 10...
Consider the data: X- 1 Y- 6 3 14 5 7 2 20 9 11 10 18 13 15 26 22 (a) Calculate the correlation between X and Y. 0.7399 (b) What percent of the variation in Y can be attributed to X? (Round to a whole percent) 55 % (c) Obtain the equation of the regression line for these data y = X +
Consider the following table of data points: Using least squares fitting, find the polynomial Q(x) of degree 2 that fit...
Consider the following table of data points:
Using least squares fitting, find the polynomial Q(x) of degree
2 that fits the data points given in the table above. Approximate
f(0.3) using Q(0.3).
f(x) i Xi 0 0.000 1.00000 1 0.125 0.98450 2 0.250 0.93941 0.375 0.86882 4 0.500 0.77880 5 0.625 0.67663 6 0.750 0.56978 0.875 0.46504 8 1.000 0.36788
f(x) i Xi 0 0.000 1.00000 1 0.125 0.98450 2 0.250 0.93941 0.375 0.86882 4 0.500 0.77880 5 0.625 0.67663...
6. (20%) Consider two random variables X and Y with the joint PMF given in Table...
6. (20%) Consider two random variables X and Y with the joint PMF given in Table 2. Table 2: Joint PMF of X and Y Y =0Y 1 X 0 X 1 0 (a) (5%) Find the PMF of X and PMF of Y. (b) (5%) Find EX, EY, Var(X), Var(Y (c) (10%)Find the MMSE estimator of X given Y, (M) for both Y 0 and Y 1
Exercise 6: Given the table of the function f(x)-2" 2 X 0 3 2 f(x) 1 2 4 8 a) Write down the Newton polynomials P1(x), P2(x), Pa(x). b) Evaluate f(2.5) by using Pa(x). c) Obtain a bound for the errors E1(x), E2(x), Es(x) Exercise 7: Consider f(x)- In(x) use the following formula to answer the given questions '(x) +16-30f+16f,- 12h a) Derive the numerical differentiation formula using Taylor Series and find the truncation error b) Approximate f'(1.2) with h-0.05...
(3.2) Consider the data given in the following table 05 1 15 f(x) 0 2 0 6 1 2 20 (4) (a) Approximate f with a function of the form q (x) = kxm (4) (b) Approximate f with a function of the form g2(x) = be Which approximation between q and g2 1s more appropriate for the given data? Justify your (3) (c) answer < In, and a piecewise cubic polynomial Consider a set of points (I,) Such that...
Consider the following data table: 0 2i = 0.2 0.4 f(xi) = 2 2.018 2.104 2.306 0.6 0.2 and 23=0.4 is The linear Lagrange interpolator L1,1 (2) used to linearly interpolate between data points 12 (Chop after 2 decimal places) None of the above. -2.50x+0.20 -5.00x+2.00 -5.00x+2.00 5.00x-1.00 Consider the following data table: 2 Ti = 0 0.2 0.4 0.6 f(x) = 2.018 2.104 2.306 0.2 and 23 = 0.4, the value obtained at 2=0.3 is Using Lagrange linear interpolation...
You are given the table below. 16 20 4 8 12 X f(x) 12 2417 6 30 Use the table and n = 4 to estimate the following. Because the data is not monotone (only increasing or only decreasing), you should sketch a possible graph and draw the rectangles to ensure you are using the appropriate values for a lower estimate and an upper estimate. 20 f(x)dx lower estimate upper estimate Estimate the area of the region under the curve...
The following y vs. x data is given x y 1 2.25|3.7 15.1 4.256 13.7 15.1 The data is fit by a quadratic spline given by ( 2.85 + 1.4x, 1< x < 2.25 f(x) = { cx? + dx +e, 2.25 < x < 3.7 (fx2 + gx + h, 3.7 < x < 5.1 The value of d most nearly is
FITTING A QUADRATIC PARABOLA 8-11 Fit a parabola (7) to the points (x, y). Using MATLAB 10. hr] Worker's time on duty, y [sec] = His/her reaction time, (t, y) (1, 2.0), (2, 1.78), (3,1.90), (4, 2.35), (5, 2.70)
FITTING A QUADRATIC PARABOLA 8-11 Fit a parabola (7) to the points (x, y). Using MATLAB 10. hr] Worker's time on duty, y [sec] = His/her reaction time, (t, y) (1, 2.0), (2, 1.78), (3,1.90), (4, 2.35), (5, 2.70)
Assuming that the first spline is linear in quadratic spline interpolation, the number of unknowns in the splines for 10 data points is QUESTION 2 The following y vs. x data is given 1 225 3.7 5.1 4.25 68615.1 The data is fit by quadratic spline interpolants given by AX) - 2.85 +1.4x, 1 5X5 2.25 AXX2dx +2.25 SX5 3.7 A x) = fx2gx+, 3.7<*5.1 The value of d most nearly is QUESTION 3 The following y vs. x data...
Consider the data: X- 1 Y- 6 3 14 5 7 2 20 9 11 10 18 13 15 26 22 (a) Calculate the correlation between X and Y. 0.7399 (b) What percent of the variation in Y can be attributed to X? (Round to a whole percent) 55 % (c) Obtain the equation of the regression line for these data y = X +
Consider the following table of data points:
Using least squares fitting, find the polynomial Q(x) of degree
2 that fits the data points given in the table above. Approximate
f(0.3) using Q(0.3).
f(x) i Xi 0 0.000 1.00000 1 0.125 0.98450 2 0.250 0.93941 0.375 0.86882 4 0.500 0.77880 5 0.625 0.67663 6 0.750 0.56978 0.875 0.46504 8 1.000 0.36788
f(x) i Xi 0 0.000 1.00000 1 0.125 0.98450 2 0.250 0.93941 0.375 0.86882 4 0.500 0.77880 5 0.625 0.67663...
6. (20%) Consider two random variables X and Y with the joint PMF given in Table 2. Table 2: Joint PMF of X and Y Y =0Y 1 X 0 X 1 0 (a) (5%) Find the PMF of X and PMF of Y. (b) (5%) Find EX, EY, Var(X), Var(Y (c) (10%)Find the MMSE estimator of X given Y, (M) for both Y 0 and Y 1
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