作者LinkJerry (§杰瑞先生§)
看板Grad-ProbAsk
標題[統計] 聯合機率函數
時間Mon Mar 16 23:33:58 2009
中原工工94年的統計
Consider an experiment of independently tossing a fair coin for n times.
Let N1 and N2, respectively, denote the number of heads and tails obtained
in the n tosses.
(a) What is the distribution of N1?
Please write down the probability mass function.
n N1 n-N1
N1~B(n,0.5) pmf:C (0.5) (0.5)
N1
(b) What is the distribution of N2?
Please write down the probability mass function.
n N2 n-N2
N2~B(n,0.5) pmf:C (0.5) (0.5)
N2
(c) What is the joint distribution of (N1, N2)?
Please write down the joint probability mass function.
這題是直接把(a)跟(b)相乘就可以了嗎?
(d) Compute Cov(N1, N2).
因為題目第一行，提到實驗獨立，所以Cov(N1, N2)=0?
(e) If the experiment is to throw a fair die, instead of a coin, let Ni
denote the number of trials that the die lands on i,
i = 1,..., 6. What is Cov(N1, N2)?
請問黃色的部份是正確的嗎? >"<...
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1F：推 MousePads:(c)不是直接相乘吧，N1和N2不是獨立的。事實上，N1和N2 03/17 00:03
2F：→ MousePads:是完全負相關(因為N1+N2=n，一個增加，另一個一定減少) 03/17 00:04
3F：→ MousePads:故f(N1,N2) = f(N1) = f(N2) (也就是同(a)或(b)的答案) 03/17 00:05