STA5107_FRADE_HW7

STA5107_FRADE_HW7 - STA5107 Dr Srivastava Homework 7 Jaime...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
STA5107: Dr. Srivastava Homework 7 Jaime Frade 1. OUTPUT a) Plot f(x) over the interval [-4,10] b) f(x) = exp(-1/2*a^2)+2*exp(-1/2*(a-3)^2)+exp(-1/2*(a-6)^2) f’(x) = -a*exp(-1/2*a^2)+2*(-a+3)*exp(-1/2*(a-3)^2)+(-a+6)*exp(-1/2*(a-6)^2) c) See code
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
STA5107: Dr. Srivastava Homework 7 Jaime Frade d)
Image of page 2
STA5107: Dr. Srivastava Homework 7 Jaime Frade
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
STA5107: Dr. Srivastava Homework 7 Jaime Frade
Image of page 4
STA5107: Dr. Srivastava Homework 7 Jaime Frade CODE %part a and part b clear all ; clc; close all % Part (a) x=[-4:0.1:10]; for i=1:length(x) Fx(i)=exp(-x(i).^2/2)+2*exp(-(x(i)-3).^2/2)+exp(-(x(i)-6).^2/2); end plot(x,Fx) % Part (b) syms a Fa=exp(-a.^2/2)+2*exp(-(a-3).^2/2)+exp(-(a-6).^2/2) diff(Fa,a) % Part c and d % % Homework 8.1 % Part c and d sigma=0.1; T = 1; N = 1000; run_times = 50; alpha = 0.995; t_small = zeros(1, run_times); for index = 1:run_times x = zeros(1, N + 1); x(1) = 10*randn; for t = 1:N y_t = x(t) + sigma*f_prime_func(x(t)) + sqrt(T*sigma)*randn; rho = min(exp((f_func(y_t) - f_func(x(t)))/T), 1); z = rand; if z < rho x(t+1) = y_t; else x(t+1) = x(t); end T = alpha * T; end t_small(index) = x(t+1); end figure(1) plot(t_small); title([ 'Evolution of the process of f(x) with run time = ' int2str(run_times)]);
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern