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UNIVERSIDADE FEDERAL DO RIO DE JANEIROINSTITUTO ALBERTO LUIZ COIMBRA DE PÓS-GRADUAÇÃO E PESQUISA DE
ENGENHARIAPROGRAMA DE PÓS-GRADUAÇÃO EM ENGENHARIA MECÂNICA
LISTA 1
Aluna: Ingrid Wendling
Matrícula: 115013564
Rio de Janeiro
2015
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clcclear allclose all x = 2*randn(1000,1)+1;histogram(x,'Normalization','pdf')hold ony = -5:0.1:10;mu = 1;sigma = 2;f = exp(-(y-mu).^2./(2*sigma^2))./(sigma*sqrt(2*pi));plot(y,f,'LineWidth',1.5)xlabel('x');ylabel('Frequência');
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Distribuição normal bi-variada
∑ ¿[ σ x2 ρ σ y
2 σ x2
ρ σ y2 σ x
2 σ y2 ]
Para realizar a decomposição de Cholesky:
syms sigx sigy psum=[sigx^2 p*sigy*sigx; p*sigy*sigx sigy^2]L=chol(sum,'lower','noCheck')
L=[ σ x❑ 0
ρ σ y❑ σ y
2 σx2−ρ σ y
❑]=[ σ x❑ 0ρσ y
❑ σ y❑√(1−ρ2)]
Para plotar o gráfico de dispersão, precisamos calcular x1 e x2:
[ x1x2]=[μ1μ2]+[ σ x❑ 0ρσ y
❑ σ y❑ √(1−ρ2)][Z1Z2]
clear allclcclose all % Dados da letra A do Probleman=1000;E=[0; 0];sigx=1;sigy=1;p=0.5; N=normrnd(0,1,[2,n]); % Variáveis normaisL=[sigx 0; % Decomposição L de Cholesky p*sigy sigy*(1-p^2)^(1/2)]; for i=1:n x(:,i)=L*N(:,i)+E;end figure(1);scatter(x(1,:),x(2,:),'.','r');title('Normal Bivariada');xlabel('x_1');ylabel('x_2');
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LETRA A
LETRA B
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clear allclose allclc %mi=E(X)=alpha*beta%sigma2=V(X)=alpha*beta2 %Mola 1ek1=10;vk1=1^2; n=200000;beta1=vk1/ek1;alpha1=ek1/beta1; %Mola 2ek2=20;vk2=4^2;n=100000;beta2=vk2/ek2;alpha2=ek2/beta2; x=gamrnd(alpha1,beta1,[1 1000]); %2x amostras do lote 1y=gamrnd(alpha2, beta2, [1 500]); %1x amostras do lote 2w=[x,y]; %união dos gama random m1=mean(x); v1=var(x); %conferência da média e variância do lote 1m2=mean(y); v2=var(y); %conferência da média e variância do lote 2 figure(1)hist(w,50)xlabel('x');ylabel('f(x)');title('Histograma da Variável Aleatória K'); u1=1./x; %cálculo de u1 dadas as v.a. de k1u2=1./y; %cálculo de u2 dadas as v.a. de k2z=[u1,u2]; figure(2)hist(z,50);xlabel('x');ylabel('f(x)');title('Histograma da Variável Aleatória U');
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close allclcclear all obs=300; %observaçõest=50; %intervalo tempoc=90; %confiança em %tt=1:1:t; %vetor tempo for i=1:obs y(i,1)=0; x=random('unif',0,1,[1,t-1]); for j=1:t-1 if x(j)<0.5 y(i,j+1)=y(i,j)-1; else y(i,j+1)=y(i,j)+1; end a=mean(y); endend figure(1)hold on;plot(tt,y);title('Random Walk 1D Simétrico'); figure(2)li=prctile(y,5); %limite inferior do envelopels=-prctile(y,95); %limite superior do envelopehold on;plot(tt,a,'r');hold on;p=zeros(obs,t);plot(tt,li,'k');plot(tt,ls,'k');title('Média e Envelope de Confiança do Random Walk 1D');legend('Média','Envelope Confiança 90%'); figure(3)y1=y(:,2);desvio1=std(y1);media1=mean(y1);hist(y1);title(strcat('Histograma para t=1 \color{red} \sigma=',num2str(desvio1),... '\color{red} média =',num2str(media1) )); figure(4)y10=y(:,11);desvio10=std(y10);media10=mean(y10);hist(y10);
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title(strcat('Histograma para t=10 \color{red} \sigma=',num2str(desvio10),... '\color{red} média =',num2str(media10) ));
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clear allclose allclc n=500;figure;hold on;for l=1:50 x=(rand(n,1)-0.5*ones(n,1)); y=(rand(n,1)-0.5*ones(n,1)); z1=zeros(n,1); z2=zeros(n,1); for i=2:n z1(i)=z1(i-1)+x(i); z2(i)=z2(i-1)+y(i); end plot(z1,z2 title('Random Walk 1D Simétrico');end
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clear allclcclose all b1=1;b2=100;x=linspace(-400,400,1001);k1=exp(-abs(x)/b1);k2=exp(-abs(x)/b2);plot(x,k1,'b', x,k2, 'r' );legend('b1 = 1','b2 = 100')xlabel('X')ylabel('K')
clear allclcclose all b=[1:1:100];K=2;N=100;C= zeros(N,N) ; x1=linspace(0,1,100);x2=linspace(0,1,100);x=[x1;x2];% ;
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for i=1:N for j=1:N sum1 =0; for k=1:K sum1 = sum1 + (( x(k,i)- x(k,j) )^2 / (b(k)^2)) ; end C(i,j) = exp ( - sum1/2 ) ; end end surf(C)