"One" 20 17 Postgraduate Entrance Examination for Mathematics-An Outline of Probability Theory and Mathematical Statistics. Do you still take the exam after the ninth chapter?

Well, if you don't take the exam, you won't have that much level, but if you have time, you should review it well. Thank you!

〈〉〉〉〉〉〉〉〉〉〉〉〉〉〉〉𝶹𝶹𝶹𝶹𝶹𝶹〉 12

Mathematics for postgraduate entrance examination, whether it is one or three, uses the same textbook.

The difference between the first and the third is:

1, Outline No.1:

Advanced Mathematics (Function, Limit, Continuity) 56%

Linear algebra (determinant, matrix, vector, linear equations, eigenvalues and eigenvectors of matrix, quadratic form) 22%

Probability theory and mathematical statistics (random events and probability, random variables and their distribution, multi-dimensional random variables and their distribution, numerical characteristics of random variables, law of large numbers and central limit theorem, basic concepts of mathematical statistics, parameter estimation and hypothesis testing) 22%

2. Three outlines:

Calculus (advanced mathematics) 56%

Linear algebra 22%

Probability theory and mathematical statistics 22%

3. Horizontal comparison:

Advanced Mathematics: The number one is the most extensive, covering the whole textbook (except the contents marked with * in Tongji Sixth Edition Advanced Mathematics Textbook), and the number three does not examine vector space and analytic geometry, triple integral, curve integral, surface integral and all applications related to physics.

Linear algebra: there is little difference between the content and examination questions of Math I and Math III.

Probability theory and mathematical statistics: No.1 has more knowledge about interval estimation and hypothesis testing than No.3, but there are still differences in examination requirements for the knowledge appearing in No.1 and No.3 outlines. For example, 1 requires understanding the conclusion and application conditions of Poisson theorem, and No.3 requires mastering the conclusion and application conditions of Poisson theorem.

(2) Extended reading of the syllabus of probability theory and mathematical statistics.

Postgraduate entrance examination for mathematics I, II and III;

1, the engineering class is Math I and Math II;

2. Economics and Management Mathematics III (before 2009, Management Mathematics III and Economics Mathematics IV, after 2009, Mathematics III and Mathematics IV were merged in the syllabus).

3, must choose a math or math two enrollment major (decided by the admissions unit):

Among the first-class engineering disciplines, such as materials science and engineering, chemical engineering and technology, geological resources and geological engineering, mining engineering, oil and gas engineering, environmental science and engineering, there are two disciplines. Whoever has higher requirements for mathematics should choose mathematics as the major and mathematics as the minor.

4. Must use mathematics three enrollment major:

First-class discipline of economics.

Business administration, agricultural and forestry economic management are in the management category.

A first-class discipline of management science and engineering, awarded a degree in management.

5. There are specific provisions on the types of test papers used by different majors.

"Three" postgraduate entrance examination, number three, probability theory and mathematical statistics, fourth edition of Zhejiang University, which contents do not belong to the outline can be omitted.

This year's postgraduate entrance examination outline hasn't come out yet. You can look at the exam content of 20 15 postgraduate entrance examination outline from the website of Zhejiang University for your reference!

ととととととととととと

20 12 came out early.

Are the evaluation criteria and interval estimation of unified measure in probability theory and mathematical statistics still tested?

Review in strict accordance with the outline, which is also the only authoritative explanation of the scope of the exam.

Review the outline and common formulas of probability theory and mathematical statistics of Lu, and kneel down! Urgent! ! !

Review outline of probability theory and mathematical statistics

First, the operation of the event.

If A, B and C are three events, A+B+C occurs at least once and ABC occurs at the same time.

AB+BC+AC appears at least twice, because it happens exactly twice.

In order to only happen once, and so on, we should be good at translating language into event operation formulas and formulas into language. ..

Therefore, if A and B are opposite events,

Second, the law of addition.

If A and B are incompatible with each other, then P(A+B)=P(A)+P(B).

For any a and b, there are

P(A+B)=P(A)+P(B)-P(AB) ( 1)

So as long as we know three of the four probabilities, P (A+B), P (A), P (B) and P (AB), we can find the remaining one.

Because B is decomposed into AB and two incompatible events,

rule

(2)

Substituting these two formulas into (1) respectively, we can get

So P(A+B), P(A) and these three probabilities can be found out as long as we know two. Similarly, P(A+B), P(B) and the remaining one can be found out as long as we know the two. For example, when P(A+B) is known,

The probability that only one of A and B will happen is

From the formula (2)

Therefore, the probability that only one of A and B will happen is

Three, the total probability formula and Bayesian formula

Let A 1, A2, … form a complete event group, then let event b have.

(full probability formula),

and

(Bayesian formula)

Among them, the most commonly used complete event group is an event A and its inverse, that is, any event A and B has it.

Usually, the experiment is imagined to be done in two steps, and the result of the first step will lead to one way or another, thus affecting the probability of whether the event B in the second step will occur. If the probability of the first step event B and the second step event B are known, and the probability of the second step event B is needed, the full probability formula is used. If the probability of event B in the second step has occurred, Bayesian formula will be used.

Fourth, random variables and their distribution

1. Discrete random variable

Univariate: p (ξ = xk) = PK (k = 1, 2, ...),

Binary: p {ξ = xk，η = yj) = pij (I，j = 1，2，...)

The relationship between marginal distribution and joint distribution;

It should be noted that when calculating the function of binary random variables, the calculated values overlap.

2. Continuous random variables

,, naturally:

The distribution function is, with

If η ~ φ (x) and η = f (η), the method of finding the probability density function of η is to find the distribution function of η Fη(x) first.

,

Then, take the derivative of Fη(x) and get the probability density function of η.

Fifth, the numerical characteristics of random variables.

Mathematical expectation:

Discrete type:

Continuous type:

Difference:

Discrete type: calculate first, then

Continuous type: calculate first

Six, several commonly used distribution

Binomial distribution

ξ~B(n, p).

It describes the probability that event A occurs k times in Bernoulli's independent test probability. Tests can be conducted simultaneously or sequentially.

evenly distribution

ξ obeying the uniform distribution on [a, b] means

If ξ obeys uniform distribution on [0, 1] and η=kξ+c, then η obeys uniform distribution on [c, k+c].

7. Unbiased estimation

The estimation of parameters is unbiased estimation, that is, generally speaking, it is unbiased estimation of Eξ and S2 is unbiased estimation of Dξ. However, when it is an unbiased estimation, it is not certain that f () is an unbiased estimation of f (), and it needs to be analyzed again.

Eight, maximum likelihood estimation

For n sample values x 1, x2, ..., xn

If the population ξ is a continuous random variable, ξ ~ φ (x; θ), likelihood function

And if the population ξ is a discrete random variable, p (ξ = xi) = p (xi; θ), likelihood function

Then solve the likelihood equation.

The maximum likelihood estimation of θ is obtained by solving.

Nine. Interval budget estimate

Under the normal population, that is, the population ξ~N(μ, σ2),

If σ2 is known, then when the test level α is given, look up the normal distribution table to find uα, and the confidence interval with confidence of 1-α is

If σ2 is unknown, where s is the square root of the sample variance (or the measured standard deviation. The confidence interval of confidence is 1-α by looking up the t distribution table to find tα.

Hypothesis test

Under the normal population, that is, the population ξ~N(μ, σ2),

Under the condition that σ2 is known, the test assumes H0: μ=μ0, and the statistic is selected. Then, under the condition that H0 holds, for a given test level α, U~N(0, 1), check the normal distribution table to determine the critical value uα, so that the value u of the statistic u calculated according to the observed value of the sample can be compared with uα, such as | u |.

If σ2 is unknown, select statistics, and when H0 hypothesis holds, T~t(n- 1), for a given test level α and sample size n, check the t- distribution table to determine the critical value tα, so that P (| t | >; Tα)=α, calculate the value of statistic T according to the observed value of the sample and compare it with Tα, such as | t| >; Tα denies H0, otherwise it accepts H0.

If it is a large sample and the t distribution is close to the standard normal distribution, you can look up the normal distribution table. At this time, it is considered that the variance of pattern book can be used as an accurate variance.

Exercises and examples to be practiced:

P5: Example 2. P6: Example 3. P226: 1，2。 P27: 20。 P59: 36，37。 P99: 1。 P28: 27，28，30。 P56: 16，65438。 15.p 164: 2，4。 p 165: 8， 1 1。 p 184: 1，2。 p235: 58，60。

Is the range of Math I and Math III in the probability statistics of Qi the same?

Although the contents of Math I and Math III are all advanced mathematics, linear algebra, probability theory and mathematical statistics, accounting for 56%, 22% and 22% respectively, the emphasis and some knowledge points to be mastered are different, which also causes some difficulty differences between Math I and Math III.

The examination of number one focuses on infinite series, curve and surface integral, which is compulsory every year and is often examined in the form of problem solving; The number three requires mastering the problem of economic application, which is basically required every year. 20 15 examines the marginal cost and elasticity in the form of solving problems, 20 14 examines the marginal income in the form of filling in the blanks, and 20 13 examines the marginal profit in the form of solving problems.

In addition to the different key knowledge, some knowledge points that need to be mastered are also different.

In advanced mathematics, mathematics one examines the physical application of spatial analytic geometry, multivariate function integral (except double integral) and calculus, while number three does not; The number three examines the economic application of calculus, while the number one does not.

In probability theory and mathematical statistics, the scope of investigation of Math 1 is slightly larger than Math 3, which mainly increases the test sites for parameter estimation, including the selection criteria of estimators, interval estimation and subsequent hypothesis testing.

Eight "Postgraduate Entrance Examination Mathematical Statistics" Zhejiang University Edition III. Probability Theory and Mathematical Statistics, which chapters are not part of the outline?

Look at the first six chapters and see where the assumptions are, with emphasis on expectations, distribution and estimation. Textbooks are just the simplest concepts and examples.

[9] Who can tell me where I can find the outline of Probability Theory and Mathematical Statistics 20 13 of Fudan University School of Management? I looked for it for a long time, but I couldn't find it. Thank you.

This is a bit difficult, and it can't be delivered to the door now. You can find it on the website of Doctor Fudan University-Postgraduate Entrance Examination. There are no further questions.

"Pick up" the number three probability theory for postgraduate entrance examination only reaches the seventh chapter (parameter estimation), right?

Yes, according to the syllabus of Mathematics III of the 20 19 Graduate Entrance Examination, the scope of investigation of probability theory and mathematical statistics includes the following parts:

Random events and probability

Random variables and their distribution

Distribution of Multidimensional Random Variables

Numerical characteristics of random variables

Law of Large Numbers and Central Limit Theorem

Basic concepts of mathematical statistics

parameter estimation

(10) Extended reading of the syllabus of probability theory and mathematical statistics;

The full mark of the third mathematics paper is 150, and the examination time is 180 minutes. The answer methods are closed book and written test. The content structure of the test paper includes: calculus, with a score of 56%; Linear algebra, with scores accounting for 22%; Probability theory and mathematical statistics, the score accounts for 22%. The question structure of the test paper is: 8 multiple-choice questions, 4 points for each question, ***32 points; Fill in the blanks with 6 small questions, with 4 points for each question and 24 points for * * *; Answer 9 small questions (including proof questions), ***94 points.