※ [本文轉錄自 NTU-Exam 看板] 作者: rabion (茱密歐與羅麗葉) 看板: NTU-Exam 標題: [試題] 95上 蕭朱杏 醫學統計學一 第一次期中考 時間: Sun Nov 19 00:39:25 2006 課程名稱︰醫學統計學一 課程性質︰必修 課程教師︰蕭朱杏 開課學院：醫學院 開課系所︰藥學系 考試時間︰2006/10/31 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1. (10 points) Explain the following: (a) What is IQR (inter-quartile range) in a boxplot? (b) How to decide the tip of the whiskers (鬍子的頂點) in a boxplot? 2. (10 points) The following data of height are collected samples from two high schools. Please examine if there is any difference between these two groups with two stem-and-leaf plots. School A={132,133,144,152,160,171,145,152,161,142,141,151,150,161,141,150}, School B={170,170,171,176,160,161,167,165,162,151,152,156,155,145,147,136} 16 2 3. (10 points) The average X is 159 for School B, and Σ(xi-159) is 1796 where i=1 xi (i=1,…,16) stands for the 16 observed values of height. (a) Please estimate the expected value of height of all students in school B and evaluate its precision. (b) If the population of height in School B is normal with known variance 100, what is the proportion that students in School B are taller than 170? (c) If the population of height in School B is normal with known variance 100, what is the proportion that students in School B are between 150 and 170? 4. (15 points) Suppose a fair dice (骰子) with six faces is tossed. (a fair dice means that each face appears with probability 1/6) (a) If the dice is tossed 3 times, what is probability that number 6 appears two times among the 3 tosses? (b) Suppose the dice is not fair, and, in fact, the number 6 appears with probability 1/100. If this dice is tossed 1000 times, what is the probability that number 6 appears at least 10 times? (c) Suppose we do not know if number 6 appears with probability 1/6 but we are allowed to toss it for 10000 times and observe the face values. What will you do then to verify if number 6 appears with probability 1/6? (d) In question (c) above, what is the population? What is the sample? 5. (10 points) When coded messages are sent, there are sometimes errors in transmission. In particular, Morse code (摩斯密碼) uses “dots” and “dashes, ” which are known to occur in the proportion of 3:4 (or, sometimes it is said that the odds of receiving dots is 3:4). (a) Suppose there is interference (干擾) on the transmission line, and with probability 1/8 a dot is mistakenly received as a dash, and vice versa. If we receive a dot, what is the probability that a dot was sent? (b) (following (a)) If we receive a dot, what is the odds that a dot was sent? 6. (10 points) What is the relative risk (RR)? It is different from odds ratio (OR). It is said that, for rare diseases, RR~OR. Why? 7. (45 points) The random pair (X, Y) has the distribution shown in the following table. (a) What is the marginal distribution of X? (b) Please derive E(X), and Var(X). (c) Are X and Y dependent? Why? (d) What is the probability that X+Y =4? (e) What is the variance of (2 X +5)? (f) What is E(X Y)? (g) What is the probability that X=2 given X+Y =4? i.e., Pr(X=2|X+Y=4)=? (h) Similar to (g) above, please derive Pr(X=1|X+Y=4) and Pr(X=3|X+Y=4), you now have the conditional distribution of X given X+Y=4. (i) Based on (g) and (h), please define E(X|X+Y=4). --

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