1. Number of questions
The national self-study exam "Advanced Mathematics (II)" contained 32 questions before June 65438+1October 2004, of which the probability statistics content was 19, accounting for 59.38%, and the total number of questions in the test paper was changed from June 65438+1October 2004 to 26 questions.
Step 2 score
Full score of National Self-taught Examination Advanced Mathematics (II) 100. Before 5438+0 in June, 2004, the total score of probability statistics in the test paper was 59, while since June, 2004 1, the total score of probability statistics in the test paper was 52. The score gap between probability statistics and linear algebra in the whole test paper has narrowed.
10 See Table 2 for the distribution and scores of probability statistics in the various questions of the national self-study exam "Advanced Mathematics (II)".
Second, the knowledge points involved in the probability and statistics questions in the test paper
1. Previous knowledge points
Location characteristics; Variation characteristics; The concepts of median, range, mode and average; The relationship between cumulative percentage function diagram and distribution function curve; Events; Event relationship; Event operation expression; Independence and compatibility; Text description of probability; Probabilistic meaning; Find the probability of events; Probability attribute; Classical probability; Conditional probability; Independent repeated testing; Sample sampling; The value of the distribution function; Integral to find the constant c; The probability density is constant; Judgment of several common distributions; Sample and population are independent and identically distributed; The calculation problem of using normal distribution properties; Expected value calculation; Calculation of expected attributes; Calculation of variance; Validity of variance; Covariance calculation; Calculation of expectation and variance of Poisson distribution; Calculation of expectation and variance of binomial distribution; Probability calculation, expectation, variance and covariance of normal distribution; Joint distribution; Joint distribution, marginal distribution table or density function, expectation calculation and independence judgment; Type determination of obeying distribution; Statistics; Chebyshev distribution; Moment estimation; Maximum likelihood estimation; Unbiased estimation; Find the confidence interval; Validity of estimator; Selection of hypothesis testing methods; Two kinds of wrong judgments in hypothesis testing: rejecting domain; Linear regression; Correlation coefficient.
2. There are already many chapters.
According to the analysis of 10 test paper, the chapters that appear frequently in the exam are: 2. 1 event and its probability; 2.2 Classical probability; 2.4 conditional probability; 3.2 Discrete random variables; 3.3 Continuous random variables; 3.4 Digital characteristics of random variables; 3.5 two-dimensional random vector; 4.3 sampling distribution; 5. Point estimation of1parameter; 5.3 Interval estimation of parameters; 6.3 Hypothesis test about normal population; 8. 1 unary linear regression.
Third, the analysis of various types of questions in the probability and statistics section
1. Multiple choice problem
From 200/kloc-0 to 2003, there were 20 multiple-choice questions in the examination paper of advanced mathematics (II), of which 12 was a probability content question, accounting for 60% of the multiple-choice questions, with a total score of 24 points. Since June 5438+ 10, 2004, the number of multiple-choice questions in the examination paper of advanced mathematics (II) has been changed to 18, in which 10 is entitled probability content, accounting for 55.56% of the number of multiple-choice questions, and the total score of probability content questions is 20 points.
10 The chapters involved in the multiple-choice questions in the test paper have the position characteristics of 1.3; Variation characteristics of 1.4; 2. 1 event and its probability; 2.2 Classical probability; 2.4 conditional probability; 3. 1 random variable; 3.2 Discrete random variables; 3.3 Continuous random variables; 3.4 Digital characteristics of random variables; 3.5 two-dimensional random vector; 4.2 Law of Large Numbers and Central Limit Theorem; 4.3 sampling distribution; 5. Point estimation of1parameter; 5.2 Criteria for excellent evaluators; 5.3 Interval estimation of parameters; 6.3 Hypothesis test about normal population; 6.6 Two types of errors in hypothesis testing; 8.2 Correlation analysis. Among them, the chapters with high frequency are: 3.4 numerical characteristics of random variables; 3.3 Continuous random variables; 5. Point estimation of1parameter; 2. 1 event and its probability; 2.2 Classical probability; 2.4 conditional probability; 3.5 two-dimensional random vector; 4.3 sampling distribution; 6.3 Hypothesis test about normal population; 3.2 Discrete random variables.
2. Short answer questions
From 200/kloc-0 to 2003, the short answer questions included 4 questions, with a total score of 16, of which 2 were probability content questions with a total score of 8. However, since June 5438+ 10, 2004, the number of short answers in the test paper has been changed to two questions, with a total score of 12, in which the probability content is entitled 1 and the score is 6.
10 There are 2.2 classical probability types in the chapters involved in the short answer to the test paper; 2.4 conditional probability; 3.2 Discrete random variables; 3.3 Continuous random variables; 3.4 Digital characteristics of random variables; 3.5 two-dimensional random vector; 4. 1 random sampling; 5. Point estimation of1parameter; 6.6 Two types of errors in hypothesis testing; 8.2 Correlation analysis. The chapters that appear more than twice are: 2.2 classical probability; 3.5 two-dimensional random vector; 2.4 Conditional probability.
Computational problem
From 200/kloc-0 to 2003, the calculation questions included 4 questions, with a total score of 20 points, including 3 probability content questions, with a score of 15. Since June 5438+0, 2004, the calculation questions in the examination paper of advanced mathematics (II) have been changed to two questions, of which the probability content is entitled 1, accounting for 8 points.
10 The chapters involved in the calculation questions in the test paper are 2.2 classical probability types; 2.4 conditional probability; 3.2 Discrete random variables; 3.3 Continuous random variables; 3.4 Digital characteristics of random variables; 5.3 Interval estimation of parameters; 6.3 Hypothesis test about normal population; 6.4 Hypothesis test of probability; 8. 1 unary linear regression.
Chapters that appear more than twice are: 8. 1 unary linear regression; 6.3 Hypothesis test about normal population; 3.3 Continuous random variables; 3.4 Digital characteristics of random variables; 5.3 Interval estimation of parameters.
Step 4 prove the problem
In the examination paper of advanced mathematics (II) before 5438+0 in June, 2004, the proof questions included two questions, with a total score of 10, of which the probability content was 1, accounting for 5 points. Since June 5438+0, 2004, the proof questions in the examination paper of advanced mathematics (II) are still two questions, but the total score has increased to 16, of which the probability content question is 1 antithesis, accounting for 8 points.
10 The chapters involved in the proof questions in the test paper include 2. 1 events and their probabilities; 2.4 conditional probability; 3.4 Digital characteristics of random variables; 3.5 two-dimensional random vector; 5. Point estimation of1parameter; 8.2 Correlation analysis. Among them, only the point estimation of the parameter 5. 1 appeared five times, and the rest appeared 1 times.
5. Comprehensive application problems
From 200 1 to 2004, the comprehensive application questions included two questions, of which the probability content was 1. From 200 1 to 2003, the total score of comprehensive application questions was 14, of which the probability content question was 7. Since June 65438+ 10, 2004, the comprehensive application questions in the test paper have been changed to 10 for each question, and the total score has been raised to 20, of which the probability content is entitled 10.
10 There are 3.3 continuous random variables in the chapters involved in the comprehensive application questions in the test paper; 3.4 Digital characteristics of random variables; 3.5 Two-dimensional random variables; 5. Point estimation of1parameter; 5.3 Interval estimation of parameters. Only 3.5 two-dimensional random variables appeared six times, and all other contents appeared 1 time.
Fourth, review the suggestions of probability statistics.
From the comparative analysis of the test papers after 2004 1 and before 2003 1, we can see that the proportion of linear algebra and probability statistics in the test paper will not change in the latest exam, that is, the whole test paper contains 26 questions, probability statistics accounts for 14 questions, and the score accounts for 52 points. The test paper is still organized around the key contents, that is, the key chapters are Chapter II Probability Statistics, Chapter III Random Variables and Probability Distribution, Chapter V Parameter Estimation, Chapter VI Hypothesis Test and Chapter VIII Regression Analysis and Correlation Analysis. Examination collection and arrangement