numerical analysis homework (limits of accuracy)
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numerical analysis homework (limits of accuracy)
Let f(x) = xn-ax"-1, and set g(x) = x". (a)...
this is numerical analysis QUESTION 1 (a) Apart from 1 = 0 the equation f(1) =...
this is numerical analysis
QUESTION 1 (a) Apart from 1 = 0 the equation f(1) = x2 - 4 sin r = 0 has another root in (1, 2.5). Perform three (10) iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations. (b) Perform three iterations of Newton's method for the function in (a) above, using x) = 1.5 as the initial (10) solution. Compare the error from the Newton's approximation...
solve using Newton Method Numerical TJ Find the mulliplicity of rock 1 f(x) = (x-1)2 inx...
solve using Newton Method
Numerical
TJ Find the mulliplicity of rock 1 f(x) = (x-1)2 inx 2 Find the order of convergence Pit en 9 digits accuracy 13 give the root of f(x) = xinx + x2 -10 f(x) = (x-2)(x-4) Find RA Por both Theo, Num. וחט P(x) = x - 1 Find R.A Theo. Num. convergence OfW= (x-2)(x+) Accelarate the at p=2, numerically secant method 13_f(x) = x3 - 2 Cosx - 17 2 significant
Let X1, . . . , Xn be independent with common density f(x) = 2x 1[0...
Let X1, . . . , Xn be independent with common density f(x) = 2x 1[0 < x < 1]. Set Vn = max(X1, . . . , Xn). (a) Verify Vn → 1 in P. (b) Show that n(1-Vn) → W in D holds for some random variable W and find the distribution function of W.
Let X1, X2,..., Xn be a r.s. from f(x) = 0x0-1, for 0 < x <1,0...
Let X1, X2,..., Xn be a r.s. from f(x) = 0x0-1, for 0 < x <1,0 < a < 0o. (a) Find the MLE of 0. (b) Let T = -log X. Find the pdf of T. (c) Find the pdf of Y = DIT: (i.e., distribution of Y = - , log Xi). (d) Find E(). (e) Find E( ). (f) Show that the variance of 0 MLE → as n → 00. (g) Find the MME of 0.
Let f and g be differentiable on R such that f(1) = g(1), and f'(x) <...
Let f and g be differentiable on R such that f(1) = g(1), and f'(x) < '() for all r ER. Prove that f(x) = g(2) for 3 >1.
Problem 4. Let X1, . . . , Xn be independent with common density f(x) =...
Problem 4. Let X1, . . . , Xn be independent with common density f(x) = 2x 1[0 < x < 1]. Set Vn = max(X1, . . . , Xn). . (b) Show that n(1 − Vn) → W in D holds for some random variable W and find the distribution function of W
Question 3 Consider the set E consisting of all quadratic polynomials of the form f(x) =ax2...
Question 3 Consider the set E consisting of all quadratic polynomials of the form f(x) =ax2 + b, where a,b ER. Let g(x) = x + 3. Find the polynomial fe e such that the distance between (f(0), f(1), f(2)) and (g(0), g(1), g(2) is minimized. What is f(1)? (Computational Check: The sum of the numerator and denominator of f(1) is 61).
i need help with these two for homework Question 26 Let f(x)=x2-1, g(x) = 3x –...
i need help with these two for homework
Question 26 Let f(x)=x2-1, g(x) = 3x – 2. Find the function. (-8)(5) of-g)(5) = 15 of-g)(5) = 10 O None of the above o-g)(5)= 11 ob-g)(5)=9 OV-8)(5) = 12 Question 27 Graph the solution set of the system. tral y<x+3 O -34 1 2 3 4 5 -3 2+ 1+ 43 1 1+ 2 3 4 5 +6 -34 + Y . +1 EI 3 777 T 7 2 1+ T...
Let X1, X2, ..., Xn be independent Exp(2) distributed random vari- ables, and set Y1 =...
Let X1, X2, ..., Xn be independent Exp(2) distributed random vari- ables, and set Y1 = X(1), and Yk = X(k) – X(k-1), 2<k<n. Find the joint pdf of Yı,Y2, ...,Yn. Hint: Note that (Y1,Y2, ...,Yn) = g(X(1), X(2), ..., X(n)), where g is invertible and differentiable. Use the change of variable formula to derive the joint pdf of Y1, Y2, ...,Yn.
this is numerical analysis please do all the questions 1. A function g(x) is called a...
this is numerical analysis please do all the questions
1. A function g(x) is called a contraction on the interval (a,b) if g([a, b]) c [a, b] and moreover, there exists 0 <k < 1 such that væ, y € [a, b] we have 19(x) – 9(y)<k|x – yl. (a) Find d > 0 such that the function g(x) = cos x is a contraction on (0.5 - 4,0.5 + d). Justify fully. Hint: The cosine of 1 radian is...
this is numerical analysis
QUESTION 1 (a) Apart from 1 = 0 the equation f(1) = x2 - 4 sin r = 0 has another root in (1, 2.5). Perform three (10) iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations. (b) Perform three iterations of Newton's method for the function in (a) above, using x) = 1.5 as the initial (10) solution. Compare the error from the Newton's approximation...
solve using Newton Method
Numerical
TJ Find the mulliplicity of rock 1 f(x) = (x-1)2 inx 2 Find the order of convergence Pit en 9 digits accuracy 13 give the root of f(x) = xinx + x2 -10 f(x) = (x-2)(x-4) Find RA Por both Theo, Num. וחט P(x) = x - 1 Find R.A Theo. Num. convergence OfW= (x-2)(x+) Accelarate the at p=2, numerically secant method 13_f(x) = x3 - 2 Cosx - 17 2 significant
Let X1, X2,..., Xn be a r.s. from f(x) = 0x0-1, for 0 < x <1,0 < a < 0o. (a) Find the MLE of 0. (b) Let T = -log X. Find the pdf of T. (c) Find the pdf of Y = DIT: (i.e., distribution of Y = - , log Xi). (d) Find E(). (e) Find E( ). (f) Show that the variance of 0 MLE → as n → 00. (g) Find the MME of 0.
Let f and g be differentiable on R such that f(1) = g(1), and f'(x) < '() for all r ER. Prove that f(x) = g(2) for 3 >1.
Question 3 Consider the set E consisting of all quadratic polynomials of the form f(x) =ax2 + b, where a,b ER. Let g(x) = x + 3. Find the polynomial fe e such that the distance between (f(0), f(1), f(2)) and (g(0), g(1), g(2) is minimized. What is f(1)? (Computational Check: The sum of the numerator and denominator of f(1) is 61).
i need help with these two for homework
Question 26 Let f(x)=x2-1, g(x) = 3x – 2. Find the function. (-8)(5) of-g)(5) = 15 of-g)(5) = 10 O None of the above o-g)(5)= 11 ob-g)(5)=9 OV-8)(5) = 12 Question 27 Graph the solution set of the system. tral y<x+3 O -34 1 2 3 4 5 -3 2+ 1+ 43 1 1+ 2 3 4 5 +6 -34 + Y . +1 EI 3 777 T 7 2 1+ T...
Let X1, X2, ..., Xn be independent Exp(2) distributed random vari- ables, and set Y1 = X(1), and Yk = X(k) – X(k-1), 2<k<n. Find the joint pdf of Yı,Y2, ...,Yn. Hint: Note that (Y1,Y2, ...,Yn) = g(X(1), X(2), ..., X(n)), where g is invertible and differentiable. Use the change of variable formula to derive the joint pdf of Y1, Y2, ...,Yn.
this is numerical analysis please do all the questions
1. A function g(x) is called a contraction on the interval (a,b) if g([a, b]) c [a, b] and moreover, there exists 0 <k < 1 such that væ, y € [a, b] we have 19(x) – 9(y)<k|x – yl. (a) Find d > 0 such that the function g(x) = cos x is a contraction on (0.5 - 4,0.5 + d). Justify fully. Hint: The cosine of 1 radian is...
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