題組內容

二、問答計算題:
 1. (25%) Consider two continuous random variables X and Y with joint pdf: 61de394e7739b.jpg

(c) (5%) Find the conditional pdf 61de398f52c52.jpg

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 (a) (5%) Find the constant c
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(b) (5%) Find the conditional pif
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(d) (5%) Find the conditional mean E[Y]X = x], forx ≥ 0
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(e) (5%) Find the conditional variance Var(Y]X = x), for x ≥ 0
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2.(10%) Let X and Y be two i.i.d. Geometric random variables with puf P(X=k) = P(Y= k)=(1 - p)k-1p, for 0 ＜ p ＜ 1 and k = 1,2,3,.... Let W = max fx, y]. Find the distribution of W.
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(a) (5%) Find the moment generating function (MGF) of X . (Please identify the domain of function)
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(b) (5%) Using MGF, find E[Xn]
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(c) (5%) Find the conditional mean E[XJX ＞ 1] Scex
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相關試卷

110年 - 110 國立中山大學碩士暨碩士專班招生考試_通訊所碩士班/甲組:機率#105733
110年 · #105733