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20082009 第一学期 概率论与数理统计（Probability and Statistics） 考试试卷（A卷）（闭卷）Name Student I D Class Date: Jan 8, 2009 Time: 8:30 am to 11:00 amInstruction: Answer all questions in the space provided. Show your work.Question 12345678totalMark ScoreQuestion 1 (21 points) Filling the blanksSignature(1). Let A, B be two events, P(A) = 0.4，P(B) = 0.3，P() = 0.6，then P() = .(2). Suppose a random variable has the probability distribution with , then = .(3). Suppose has the joint density function , then the marginal distribution for alone = . (4). Suppose ，consider a quadratic equation with one unknown about y, if the probability of this equation having no real root is , then .(5). The number of distinct permutations can be made from the letters of the word access = .(6). Let be a random sample of size n taken from population, , then .(7). Let be a random sample of size n taken from population ,and are unknown , if is a confidence interval for with confidence level , then k = .ScoreQuestion 2 (18 points) Choosing the only one right resultSignature(1). Suppose, , if and are independent, then ( )(A) (B) (C) (D) (2). Suppose X N( 3, 4 )，Y E( 5 ) , find the error result ( )(A) (B) (C) (D) (3). Suppose that random variables and are independent, if they have the same probability distribution with, then ( )(A) 2/3 (B) 1 (C) 1/2 (D) 5/9 (4). Suppose, and , if ,then ( )(A) s1s2 (C) m1m2(5). Let be a random sample of size n taken from population ,，, then the following random variables which one is the t-distribution with n-1 degrees of freedom. ( )(A) (B) (C) (D) (6). Suppose, , then = ( )(A) 1 (B) -1 (C) 1/2 (D) 0ScoreQuestion 3: (12 points)SignatureSuppose a random variable X has the density function. Observe independently for three times, let denote the number of an eventoccurring in three times, determine:(1) the probability distribution of ;(2) the probability distribution of .ScoreQuestion 4 (14 points)Signature Suppose has the joint density function as follows: .(1)Find the constant c;(2) Are X and Y independent?(3) Determine the conditional distribution of X for any given value of Y.(4)ScoreQuestion 5 (10 points)SignatureSuppose that a box contains one fair coin and one coin with a head on each side. Suppose also that one coin is selected at random and tossed, a head is obtained. Determine:(1) the probability of this event occurring ;(2) the probability that this coin is the fair coin when the above event occurred.ScoreQuestion 6 (5 points)SignatureThere are 4 girls and 8 boys take part in interview of some company. Suppose that the interviewer select one student randomly every time, determine the probability that there are just 2 boys waiting for interviewing when all the girls have interviewed.ScoreQuestion 7 (12 points)SignatureSuppose a random variable X has the density function , let, determine:(1) the joint probability distribution of (Y, Z) ;(2) D(Y+Z).ScoreQuestion 8 (8 points)SignatureSuppose a population has the density function , where is unknown parameter. Let be a random sample of size n taken from population, find the maximum likelihood estimator for .第 8 页 共 8 页
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