課程名稱︰機率導論
課程性質︰必修
課程教師︰陳鵬文
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2011/06/02
考試時限（分鐘）：30分鐘
是否需發放獎勵金：是
試題 :
1. Suppose that the joint density of Ｘ and Ｙ is given by
exp(-x/y) exp(-y)
f(x,y) = ------------------- , 0 < x < ∞ , 0 < y < ∞ .
y
Compute E[Ｘ|Ｙ=y].
2. Let Ｘ be the number of 1's and Ｙ the number of 2's that occur in n rolls
of a fair die.
Compute the correlation ρ(Ｘ,Ｙ).
3. A group of 16 people consisting of 8 men and 8 women is randomly arranged
into 8 pairs of 2 each.
Compute the expectation and variance of the number of pairs thaht consist
of a man and a woman.
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