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Mathematical Statistics Assignment

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Added on  2020-05-28

Mathematical Statistics Assignment

   Added on 2020-05-28

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Running head: STATISTICS 1STATISTICS <Name of Student > <Institutional Affiliation > <Instructor’s Name > <Date of Submission >
Mathematical Statistics Assignment_1
STATISTICS 2Question 33. Consider the problem; min (x-y) ^2+2(y-2)a) Verify that the problem has multiple optima.By finding the derivative of the equation in which we find x where y is minimum we have;dy/dx = [x^3-y]^2 + 2[y-x]^4dy/dx = [x^6-y^2] = 2[y^4-x^4]dy/dx = x^6-y^2+2[y^4-x^4]6x^5-2yyʹ+2[4y^3yʹ-4x^3]6x^5-2yyʹ+8y^3yʹ-8x^36x^5-8x^3=2yyʹ-8y^3yʹ6x^5-8x^3=yʹ[2y-8y^3]fʹ(x)= (6x^5-8x^3)/(2y-8y^3)= 6x^5-8x^3fʹʹ(x) = 30x^4-24x^2fʹʹʹ (x) =120x^3-48xfʹʹʹ(x) = 360x^2-48For minimum optimality, the value of y=0 give;(6x^5-8x^3)/(2y-8y^3) = 0(6x^5-8x^3)=0Hence X= 2 and 0Therefore from the above calculations, the problem has multiple derivatives.b) Use Newton’s method to solve the problem starting with the initial points Xt=[1.25,0.75], Xt=[0.5,0.5] and Xt=[0.5,-0.5]. In table, print the minimum, the value of the function at the minimum, and the number of iterations needed to reach an approximation of the minimum with an accuracy of atleast 4d.p.Study and explain the pattern of convergence for each initial point. The Newton method for finding a root of an equation is given by; Xk= fʹ(x)/fʹʹ(x)Table 1. Summary of iterations IterationXifʹ(x)fʹʹ(x)fʹʹ(x)fʹʹʹ(x)
Mathematical Statistics Assignment_2

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