[課業] 數理統計
黃老師3.2節提到獨立r.v有加成性,但均勻分配並不具備.我的做法是先求joint.m.g.f
Mx,y(s,t) = (e^s - 1)/s‧(e^t - 1)/t , where X～U(0,1) Y～U(0,1) 且獨立
又 marginal.p.d.f Mx(s) = Mx,y(s,0) , My(t) = Mx,y(0,t) 不存在
故由m.g.f的唯一性定理知X+Y並不服從均勻分配.
請問這樣對否?
另外請問m.g.f的唯一性定理對隨機向量亦成立嗎?
在老師書上定理2.4對幾何分配的加成性提及:
若Xi有自0開始的Ge(p)則ΣXi～NB(r,p), where i=1,2....,r
請問何謂"自0開始"?又一般考試用書對此定理使用條件更強:i.i.d,是為了處理"自0開始"?
謝謝!
(先預祝劉老師端午佳節快樂!)
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