Given Fxy(x,y)=u(x)u(y)[1-Exp(-x/2)-Exp(-y/2)+Exp(-(x+y)/2)]. Note: The step functions mean that Fxy(x,y)=0 for either or both x<0 and y<0....

Given Fxy(x,y)=u(x)u(y)[1-Exp(-x/2)-Exp(-y/2)+Exp(-(x+y)/2)]. Note: The step functions mean that Fxy(x,y)=0 for either or both x<0 and y<0. Any x or y argument range below zero must be truncated at zero. Determine:
a) P{X<=1,Y<=2} Ans: 0.2487
b) P{0.5<X<1.5} Ans: 0.3064
c) P{-1.5<X<=2, 1<Y<=3} Ans: 0.2423

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orchestra answered 1 year ago

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u''-2u'-8u=0 u(0)= α， u'(0)=2π y''+9y'=cosπt, y(0)=0, y'(0)=1

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