《概率论与数理统计》概率论2009春双语.docVIP

诚信应考,考试作弊将带来严重后果！ 华南理工大学期末考试 《 Probability Statistics》试卷A(09-1)jsj 注意事项：1. 考前请将密封线内填写清楚； 2. 所有答案请直接答在试卷上(或答题纸上)； 3．考试形式：闭卷； 4. 本试卷共10题，每题10分，满分100分， 考试时间120分钟。 题 号 1 2 3 4 5 6 7 8 9 10 Total 得 分 评卷人 z v =0.005 =0.025 v =0.05 =0.01 0.15 0.56 17 2.898 2.11 1 3.841 6.635 1.645 0.95 18 2.878 2.101 2 5.991 9.210 1.75 0.96 1.96 0.975 1. If 3 dice are thrown, find the probability that (a) all 3 will show fours; (b) all 3 will be alike; (c )2 will show fours and the third something else; (d) only 2 will be alike; (e) all 3 will be different. 2. It is known that P (A)=0.6, P (B)=0.8, show that ) (b)If two dice are thrown repeatedly, find the probability of obtaining a 9 before a 6 turns up. 3. In a class election there are two parties. John is nominated by one party, and the probability that he will be elected is 3/4, provided Willian is not nominated by the opposition. The probability that Willian will not be nominated is 1/3 and the probability that he will be elected if nominated is 2/3. What is the probability that John will be elected. 4． In an entertaining TV program, members of the audience are selected to play a game. Four cards, numbered 1, 2, 3 and 4 , are put in random order with faces down. The person selected is requested to guess the numbers on the cards one after another. The game is over as soon as either he makes a wrong guess or he has made all correct guesses. He will be given $24 for a wrong guess on the first card, $240 on the second card, $480 on the third card. and $960 if he makes all correct guesses. The amount of money that can be won is denoted by X, find the probability distribution of X. find the mean and variance of X. Let m and denoted, respectively, the mean and variance of X. It is known that for any t 0, P{ (X– m )2 t } Deduce that for any k 0, P{ m – kX m + k} 1– (d) Let T be the total payoff for 1