设随机变量X的概率密度f(x)=(1/2)e-|x|，(-∞＜x＜+∞)．求E(X)，D(X)．
由于f(x)为偶函数，xf(x)为奇函数，所以有 E(X)=∫+∞-∞xf(x)dx=0． D(X)=E(X2)-(E(X))2=∫+∞-∞x2f(x)dx-0 =1/2∫+∞-∞x2e-|x|dx=1/2(∫0-∞x2exdx+∫+∞0x2e-xdx) =1/2(x2ex-2xex+2ex)|-∞0+1/2(-x2e-x-2xe-x-2e-x)|+∞0 =1+1=2．
设随机变量X的概率密度f(x)=(1/2)e-|x|，(-∞＜x＜+∞)．求E(X)，D(X)．
由于f(x)为偶函数，xf(x)为奇函数，所以有 E(X)=∫+∞-∞xf(x)dx=0． D(X)=E(X2)-(E(X))2=∫+∞-∞x2f(x)dx-0 =1/2∫+∞-∞x2e-|x|dx=1/2(∫0-∞x2exdx+∫+∞0x2e-xdx) =1/2(x2ex-2xex+2ex)|-∞0+1/2(-x2e-x-2xe-x-2e-x)|+∞0 =1+1=2．
