0910下概率双语A试卷WithAnswer.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 《概率统计（双语）》试卷A 2009－2010学年度下学期 注意事项：1. 考前请将密封线内各项信息填写清楚； 2. 所有答案请答在试卷，答题卷上。 3．考试形式：闭卷； 满分：100分 4．考试时间120分钟。 题 号 1 2 3 总分 分值 25 60 15 得 分 评卷人 1．FILLING THE BLANKS (25 points) (1) In a bag there m white balls and n black balls with m+n2. If we draw one ball from the bag, the probability of the ball being a white one is . If we draw two balls from the bag, the probability that two balls are all white is . If we draw the ball one by one from the bag without replacement, the probability that the second ball drawn is white is . (2) If the probability density of a random variable X is given by , 1/3 , the probability for X to take a value between 0.5 and 1.5 is 7/8 . (3) Suppose D(X)=36, D(X-Y)=62, D(X+Y)=42. Then the correlation coefficient -5/24 . (4) If a random variable has mean and standard deviation , Chebyshev’s theorem tell us that . (5) Suppose Y=2X+1, , Thus . (6) Let be a distribution with degree , then . (7) Let be a variable following an exponential distribution with mean , the density function of is . (8) Let , and are independent, is an -distribution with degree and , i.e. . 2. COMPUTATIONS: (60 points) (1). There are 4 white balls and 6 black balls in a bag. A ball is drawn at random from the bag and a ball of another color is then put into the bag. Then a second ball is drawn. If the two balls drawn are of the same color, what is the probability that they are both black? Solution: set and as the events of the two balls are all black, white, and of the same color, respectively. Then , Thus the probability is . (2). A supermarket is doing an ad compaign by organizing a lucky raffle draw for every 100 purchasers. The rules is that every one write his own name on a card, put the card into a lottery box, thus there are 100 names in the box. Now every one draw a card from the box without replacement, one by one. The one who draw the card with his own name get a 50%