D(X)=E(X^2)-[E(X)]^2
而
E(X)=∫xf(x)=∫1/2*xe^-|x|,-∞<x<+∞
=∫1/2*xe^x -∞<x<0 +∫1/2*xe^-x 0<x<+∞
=1/2*xe^x-1/2*e^x -∞<x<0
+∫1/2*xe^-x+1/2*e^-x 0<x<+∞
=-1
E(X^2)=∫x^2f(x)=∫1/2*x^2e^-|x|,-∞<x<+∞
=∫1/2*x^2e^x -∞<x<0 +∫1/2*x^2e^-x 0<x<+∞
=1/2*x^2e^x-x*e^x+ e^x -∞<x<0
+∫1/2*x^2e^-x+x*e^-x+e^-x 0<x<+∞
=3
则D(X)=E(X^2)-[E(X)]^2=2
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