第二章 多元正态分布及参数的估计

clear;x=-8:0.5:8;            %定义自变量x的一维刻度向量

y=x';                        %定义自变量y的一维刻度向量

X=ones(size(y))*x;        %计算自变量平面上取值点坐标的二维数组

Y=y*ones(size(x));        %计算自变量平面上取值点坐标的二维数组

Z=1/(2*pi)*exp(-0.5*((X).^2+(Y).^2));

mesh(Z);    

                 图2.1 

contour(Z,10)

             图2.1 等高线

Z=1/(2*pi*sqrt(1-0.75^2))*exp(-0.5/(1-0.75^2)*(X.^2+Y.^2-2*0.75*X.*Y));

mesh(Z);

                图2.2

contour(Z,10)

              图2.2 等高线

Z=1/(2*pi*2*sqrt(1-0.75^2))*exp(-0.5/(1-0.75^2)*((X/2).^2+Y.^2+2*0.75*(X/2).*Y));

subplot(1,2,1),mesh(Z)

subplot(1,2,2),contour(Z,10)

                   图2.3 

习题二

2-19题

样本数据：x=[65 45 27.6;70 45 30.7;70 48 31.8;69 46 32.6;66 50 31;67 46 31.3;68 47 37;72 43 33.6;66 47 33.1;68 48 34.2]

样本均值向量：m=mean(x)'

m =

   68.1000

   46.5000

   32.2900

样本离差阵：A=(10-1)*cov(x)

A =

   42.9000  -17.5000   17.4100

  -17.5000   34.5000    5.5500

   17.4100    5.5500   55.7090

样本协方差阵：s=cov(x)

s =

    4.7667   -1.9444    1.9344

   -1.9444    3.8333    0.6167

1.9344    0.6167    6.19

样本相关阵：corr=corrcoef(x)

corr =

    1.0000   -0.4549    0.3561

   -0.4549    1.0000    0.1266

    0.3561    0.1266    1.0000