设随机变量X的概率密度
F(x,y)=
{1+x,-1≤x≤0;
1-x,0﹤x≤1;
0其他．
求D(X)．
D(X)=E(X2)-(E(X))2．而 E(X2)=∫+∞-∞x2f(x)dx=∫0-1x2(1+x)dx+∫10x 2(1-x)dx=[(1/3)x3+(1/4)x4]0-1+[(1/3)x3+(1/4)x4]10=1/6 E(X)=∫+∞-∞xf(x)dx=∫0-1x(1+x)dx+∫10(1-x)dx=0．所以 D(X)=E(X2=)-(E(X))2=1/6．
设随机变量X的概率密度
F(x,y)=
{1+x,-1≤x≤0;
1-x,0﹤x≤1;
0其他．
求D(X)．
D(X)=E(X2)-(E(X))2．而 E(X2)=∫+∞-∞x2f(x)dx=∫0-1x2(1+x)dx+∫10x 2(1-x)dx=[(1/3)x3+(1/4)x4]0-1+[(1/3)x3+(1/4)x4]10=1/6 E(X)=∫+∞-∞xf(x)dx=∫0-1x(1+x)dx+∫10(1-x)dx=0．所以 D(X)=E(X2=)-(E(X))2=1/6．
