Re: [問題] 二元常態問題
f(x,y)=
1 1
_________ exp{-___________ *[(x-3)^2/4 - 2*0.6*(x-3)/2*(y-2)/1 + (y-2)^2/1]}
2π*2*1 2(1-0.6^2)
let z=x+y => x=z-k , |J|=1
k=y y=k
1 -1
f(z,k)= ________ * exp {(________)*[(z-k-3)^2/4 - 0.6(z-k-3)(k-2) + (k-2)^2]}
4π 1.28
∞
f(z) = ∫ f(z,k) dk
-∞
然後在求mgf
※ 引述《kevin20250 (喔喔)》之銘言：
: X,Y ~BVN
: ux = 3 σx = 2
: uy = 2 σy = 1
: ρ=0.6
: find the moment-generating function of Z = X + Y
: 想了很久還是不會= ="
: 想問怎麼解...謝謝
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