[生醫] [統計]-分配

看板Grad-ProbAsk作者 (travor )時間15年前 (2010/10/12 14:05), 編輯推噓5(5推 0噓 18→)
留言23則, 4人參與, 7年前最新討論串1/1
題目: According to the Massachusetts Department of Health, 224 women who gave birth in the state of Massachusetts in 1988 tested positive for the HIV antibody. Assume that , in time , 25% of the babies born to such mothers will also become HIV-positive. (a) If samples of size 224 were repeatedly selected from the population of children born to mothers with the HIV antibody, what would be the mean number of infected children per sample? Ans. Mean = np = 224 * 25% = 56 the mean number of infected children per sample = 56 (b) What would be the standard distribution? Ans. 請問版上統計高手,這題是要問哪一種distribution? Poisson distribution? 那我答案應該直接寫distribution的類別嗎? (c) Use Chebychev’s inequality to describe this distribution. Ans. 這題完全不會@@" 因為根本不知道題目要問什麼?? =..=" Chebychev’s inequality我google完還是不懂阿 囧 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 118.171.129.6 ※ 編輯: travor 來自: 118.171.129.6 (10/12 14:06)
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10/12 15:12, , 1F
(b)有n,有p 看來是二項分配
10/12 15:12, 1F
推
10/12 15:15, , 2F
(c)試試中文 "柴比雪夫不等式"
10/12 15:15, 2F
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10/12 23:45, , 3F
個人淺見
10/12 23:45, 3F
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10/12 23:45, , 4F
由題意得知
10/12 23:45, 4F
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10/12 23:45, , 5F
X1,X2,...,X224~ber(p=0.25)
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10/12 23:46, , 6F
且令Y=X1+X2+...+Xn~B(n=224,p=0.25)
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10/12 23:47, , 7F
故(a)E(Y)=np=224 x 0.25=56
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10/12 23:47, , 8F
(b)因為Var(Y)=npq=224 x 0.25 x 0.75=42
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推
10/12 23:55, , 9F
故Y標準差為根號42=6.48
10/12 23:55, 9F
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10/12 23:55, , 10F
且由柴比雪夫不等式得知
10/12 23:55, 10F
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10/12 23:57, , 11F
P(|Y-E(Y)|<=k x 標準差)>=1-1/k*2
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10/12 23:59, , 12F
=>P(|Y-56|<=k*6.48)>=1-1/k^2
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10/13 00:01, , 13F
感謝兩位大大熱心提供思考方向!小的叩謝!
10/13 00:01, 13F
推
10/13 00:02, , 14F
故當k=2時，至少有1-1/2^2=0.75的機率受感染的孩童數介
10/13 00:02, 14F
推
10/13 00:04, , 15F
於43.04個人到68.96個人
10/13 00:04, 15F
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10/13 00:06, , 16F
且當k=3時，至少有1-1/3^2=0.889的機率受感染的孩童數
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10/13 00:06, , 17F
介於36.56個人到77.44個人
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10/13 00:07, , 18F
PS:(c)小題最後的人數範圍~有可能需要做轉換為整數
10/13 00:07, 18F
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10/13 00:08, , 19F
且其中有些符號用錯~非常抱歉
10/13 00:08, 19F
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10/13 01:15, , 20F
非常感謝k大的傾囊相授!!!!<(_ _)>
10/13 01:15, 20F
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08/09 10:45, , 21F
且令Y=X1+X2+. https://muxiv.com
08/09 10:45, 21F
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09/11 14:00, , 22F
(b)有n,有p 看來 https://daxiv.com
09/11 14:00, 22F
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12/15 00:25, 7年前 , 23F
故(a)E(Y)=np https://muxiv.com
12/15 00:25, 23F
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