1: conditional probability (total probability formula, Bayesian formula and binomial probability formula are mainly related to the things in the later chapters)

2. In the distribution of random variables:

① Discrete type

Principal binomial distribution and Poisson distribution

② continuous type

Grasp the uniform distribution and exponential distribution, and remember their distribution function expressions.

Know how to find the probability density of continuous random variables, and remember the uniform distribution and exponential score.

Probability density and normal distribution of cloth distribution function

3. Multidimensional random variables master two-dimensional random variables, find their marginal probability density, and know how to learn the previous one-dimensional average.

Two-dimensional uniform distribution and normal distribution are not difficult to understand, just look at the explanation in the book. Focus on the back.

The distribution of "harmony" and "maximum and minimum" can be understood by doing it several times in practical problems. Convolution formula is the key.

4. Seven common distributions and distribution lists or probability densities of mathematical expectations and variances should be memorized.

5: covariance, correlation coefficient, this piece is easy to read; Chebyshev inequality, remember.

6. Chi-square distribution, T distribution and F distribution, remember how they are defined, remember the expression, expectation and variance of Chi-square distribution.

7. Moment estimation and maximum likelihood estimation are the key points of parameter estimation, and the general test probability will have great problems; Interval estimation usually

It is much more convenient to make one or two small questions and remember a few established conclusion formulas.

How to learn probability theory?

The most difficult part of probability theory is the basic knowledge, which mainly involves four parts: permutation and combination, derivative, integral and limit. Now let me analyze this part for you. To say that this part is the foundation itself shows that this knowledge is not the content of probability statistics research, but only some indispensable tools for learning probability statistics. In this case, we will not make too much investigation on this part of the content in the exam, and we will try our best to avoid losing points in these aspects. At this point, it is necessary to point out some people's "tactical mistakes" in learning this course. Some people have made great efforts to learn calculus, even before learning probability and statistics, it is not advisable to learn calculus again. For this part of the content, choose the knowledge involved in the textbook to review and understand. Never let basic knowledge become an obstacle to probability and statistics. You should know which is the key and which is the difficult point in your study.

How to master problem-solving skills? As the saying goes, "no one is perfect", for the course of mathematics, it is more appropriate to use another idiom to describe it-"knowledgeable" For our self-taught candidates, the study time is short, and it is unrealistic to use "who makes who is perfect", but "well-informed" can indeed be done in a short time. In other words, in normal times, you can't blindly do more questions. The key is to do more questions, not quantity, but more importantly. The same knowledge point can be examined from many angles. Some students have done many topics of the same type because of the problem of choosing counseling books, but they have little contact with the types of topics. I feel depressed during the exam. So how should we master the topic type? I think real questions over the years are our best choice.

How to practice at ordinary times? This question may be incredible to many people. There is a saying that "habit forms character". This sentence also applies to our research. Over the years, some people have good study habits. Although their study foundation is not good and their study time is limited, they can persist in learning according to the learning rules they know, and can think and make progress according to the instructions of their teachers. Most of us are lazy. If we can't read a question at a glance, we will find the answer soon. Read the answer, that's it. When I feel clear, I put it down. In this way, "I broke a lot of corn, and finally there was only one corn left." We know very well that the best way is to choose one and keep one. Even if you only pick two along the way, you will gain more than those who pick them in a hurry but don't know what to keep. Usually, you should think more, sum up more, do one thing at a time, and often review the questions you have done, so as to master knowledge. As far as my consulting experience is concerned, most people still have problems on this issue.

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