98 99 國安局統計學考題 - 考試

: 99題目
: http://imgur.com/iwEZ5c3
: http://imgur.com/GP4ddnU

: 99參考解答
: http://imgur.com/1CCQBR3

第五題
f(x,y) = exp(-y)/y 0<x<y, 0<y<∞

E(X^3|y=2) = ∫x^3*f(x|y=2)dx

f(x|y) = f(x,y)/f(y) = f(x,y)/∫f(x,y)dx

又∫f(x,y)dx

=∫_{0,y} exp(-y)/y dx

= [exp(-y)/y]*∫_{0,y} 1 dx

= [exp(-y)/y]*y = exp(-y)


f(x|y) = f(x,y)/∫f(x,y)dx

= [exp(-y)/y]/[exp(-y)]

= 1/y 0<x<y

f(x|y=2) = 1/2, 0<x<2

E(X^3|y=2)

= ∫x^3*f(x|y=2)dx

= ∫_{0,2}x^3*(1/2)dx

= (1/2)*x^4/4|_{0,2}

= 2
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