江西财经大学概率论与数理统计试卷2007Probability(C)

江西财经大学
06－07学年第二学期期末考试试卷
试卷代码：12104C 授课课时：64
课程名称：概率论Probability and Statistics 适用对象：2005级国际学院
试卷命题人 李杰 试卷审核人
1. Fill in the blanks (3 points ×5=15 points)
(1)Suppose 3'=P(A ).,4=P(B ).,)(B A P '=.5,then 'P(B |A B )=
(2)The area under the standard normal curve between -1000 and 1.645 is
(3) A sample n 21X ,,X ,X ⋯drawn from population ),(N ~X 10. ,X n X n
i i ∑==1
1
∑=--=n i i )X X (n S 1
22
11, then 22+=E(S X ) (4) A continues rv X is said to have a normal distribution with parameters 2μσand , then the pdf of X is
(5) The population has
Set the mean value of a random sample is 1.5, then the moment estimate of parameter θ is
2. There are four choices in each question, but only one is correct. You should choose the correct one into the blank. (3 points ×5=15 points)
(1). For any events A and B with ⊂A B , then the correct statement is ( ) （A ）-=-P(B A)P(B )P(A) （B ）=P(B|A)P(B ) （C ）=P(A B )P(B ) （D ）=P(A)P(A B )
(2). The joint pmf of X and Y appears in the accompanying tabulation:
if X （A ）92=α，185=β（B ）91=α，187=β（C ）41=α，41=β （D ）61=α，3
1
=
β
(3). If X follows a normal distribution ，1-=EX ，23=EX ，),,,(21n X X X is a simple
sample drawn from the population X , then the distribution of ∑==n
i i X n X 1
1is （ ）
（A ）21-N(,)n
（B ）12-N(,)n n （C ）)4,1(n N - （D ）)4
,1(n
n N -
(4).If X and Y are uncorrelated, X and Y have a Possion distribution with parameter λ=2, then 321--V(X Y ) is （ ）
（A ）1 （B ）9 （C ）26 （D ）25
(5).In tests about a normal population mean(μ)，the null hypothesis 00:μμ=H can be
rejected at significance level α=0.05, if selected significance level α=0.01，the decision is （ ）
（A ）0H cannot be rejected （B ）either 0H cannot be rejected or 0H should be rejected （C ）0H should be rejected （D ）0H cannot be rejected and 0H should be rejected
3. (10 points ) Consider three independent events 1A ,2A ,3A , and let 4
=
i i
P(A ) for 123=i ,,. Express the probability that at least one of these three events occurs and do the same for the probability that at least two of the events occur.
4. (10 points ) A man takes either a bus or the subway to work with probabilities .4 and .6, respectively, when he takes the bus, he is late 25% of the days. When he takes the subway, he is late 20% of the days. If the man is late for work on a particular day, what is the probability that he took the bus?
5. (10 points )A college professor never finishes his lecture before the bell rings to end the period and always finishes his lectures within 4 min after the bell rings. Let X =the time that elapses between the bell and the end of the lecture and suppose the pdf of X is
2
30464
⎧≤≤⎪=⎨⎪⎩x
x f (x )otherwise a. Obtain the cdf (cumulative distribution function) of X . (Hint: give an expression for )x X (P ≤) b. Compute 31+E(X )
6. (10 points ) A certain market has both an express checkout line and a superexpress checkout line. Let 1X denote the number of customers in line at the express checkout at a particular time of day and let 2X denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of
X and X is as given in the accompanying table.
12b. What is 122>P(max(X ,X ))?
c. What is 22EX
7. (10 points ) Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is
1201
0θθ+⎧+≤≤=⎨
⎩
()x x f (x )otherwise , where 2θ-<.A random sample of five students yields data 19=x .，28=x .，37=x .，46=x .，59=x .. Obtain the maximum likelihood estimate of θ for the given data. ( Hint: 2722ln(.)＝－1.3)
8. (10 points ) A random sample of n=100 observations has a mean x =9.1 and a standard deviation s =3.9. Find a 95% confidence interval for μ.
9. (10 points ) The melting point of each of 16 samples of a certain brand of hydrogenated
vegetable oil was determined, resulting in x =96.32. Assume that the distribution of melting point is normal with σ=1.20. Test 0H :μ=95 versus a H :μ≠95 using a two-tailed level α=.05.
Table:。