求E(X+Y).设(X,Y)的概率密度为... 设(X,Y)的概率密度为 f(x,y)=e^(-y),0=
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E(X+Y)=∫∫(x+y)f(x,y)dxdy
=∫∫xf(x,y)dxdy+∫∫yf(x,y)dxdy
=∫[0,1]xdx∫[0,+∞]e^(-y)dy+∫[0,1]dx∫[0,+∞]ye^(-y)dy
=1/2+1=3/2.
∫[0,+∞]ye^(-y)dy
=-ye^(-y)|[0,+∞]+∫[0,+∞]e^(-y)dy.[分部积分]
=0+[-e^(-y)]|[0,+∞]
1.
=∫∫xf(x,y)dxdy+∫∫yf(x,y)dxdy
=∫[0,1]xdx∫[0,+∞]e^(-y)dy+∫[0,1]dx∫[0,+∞]ye^(-y)dy
=1/2+1=3/2.
∫[0,+∞]ye^(-y)dy
=-ye^(-y)|[0,+∞]+∫[0,+∞]e^(-y)dy.[分部积分]
=0+[-e^(-y)]|[0,+∞]
1.
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