hw11sol - IEOR 4404 Assignment #11 Solutions Simulation...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: IEOR 4404 Assignment #11 Solutions Simulation 16th December 2006 Prof. Mariana Olvera-Cravioto Page 1 of 4 Assignment #11 Solutions 1. clear all; N=10; lamda=1/2; for i=1:N U=rand; E(i)=0-(1/lamda)*log(U); end X=sort(E,ascend); for i=1:N D1(i)=i/N-(1-exp((-1)*X(i)/2)); D2(i)=1-exp((-1)*X(i)/2)-(i-1)/N; end Dn=max(max(D1),max(D2)) %calculate Dn for 10 exponential variables SS=100000; %sample size I=0; for j=1:SS for i=1:N U(i)=rand; end Y=sort(U,ascend); for i=1:N D1(i)=i/N-Y(i); D2(i)=Y(i)-(i-1)/N; end if max(max(D1),max(D2))>Dn I=I+1; end end PValue=I/SS %P-Value 2. (a) We need to use Y = 2 - Z =- Z as an antithetic variable. Please refer to the code in part b. (b) %using raw estimator clear all; N=1000000; for i=1:N Z=randn; X(i)=(Z^3)*exp(Z); end mean(X) std(X) %using antithetic variables for i=1:N Z=randn; Y(i)=((Z^3)*exp(Z)-(Z^3)*exp((-1*Z)))/2; end mean(Y) std(Y) 2 IEOR 4404, Assignment #11 Solutions error=1.960201*std(Y)/(N^0.5) 3. (a) As in the notes, we compute c * as follows: c * =- cov ( I,X ) var ( X ) Now, cov ( I,X ) = E [ IX ]- E [ I ] E [ X ]. And, E [ IX ] = E [ IX | X a ] P [ X a ] = E [ X | X a ] P [ X a ] = a . And, E [ I ] E [ X ] = a 1 / 2 = a/ 2. Substituting, we get that cov ( I,X ) = a/ 2....
View Full Document

Page1 / 4

hw11sol - IEOR 4404 Assignment #11 Solutions Simulation...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online