First, grasp the core clues of the discipline.
The core thread of probability theory and mathematical statistics is distribution and numerical characteristics, so two big questions are generally selected from the following three aspects:
1, the distribution and numerical characteristics of one-dimensional random variables and their functions
2. Distribution and numerical characteristics of two-dimensional random variables and their functions.
3. Distribution and numerical characteristics of point estimation (moment estimation, maximum likelihood estimation) and statistics.
Second, the characteristics of probability and statistics proposition
Looking at the real questions of probability statistics in recent ten years, we find that probability propositions attach importance to the following contents:
1, comprehensive high number: the development of modern probability statistics is inseparable from advanced mathematics and calculus knowledge. Probability and statistics questions are also inseparable from calculus knowledge. For example, to find the probability of a point with a distribution function, you need to use the left limit of the distribution function. Summation of series will be used to find the digital characteristics of discrete random variables, and integration will definitely be used to find the digital characteristics of continuous random variables.
2. Classification discussion: for example, the distribution of one-dimensional and two-dimensional random variable functions, the synthesis of two-dimensional discrete random variables and continuous random variables, etc. In general, we need to discuss in categories, without repetition or omission, which requires us to construct a complete event group for complete set decomposition.
3. Combination of numbers and shapes: Many problems in probability theory also have obvious geometric significance, such as probability density, distribution function, symmetry of normal distribution and geometric significance of distribution function. If we can make full use of geometric meaning, it will greatly improve the speed of solving problems, simplify the complex and improve the accuracy.
4. The correct difficulty is opposite: in the process of dealing with high probability problems, if you encounter difficulties and can't continue to do it, students should learn to think from the opposite side. Generally, complex problems are often simple, and positive difficulties are the opposite. Examine students' flexibility.
5. Probabilistic thinking: In recent years, we have found that probabilistic thinking has become more and more prominent, that is, we can spell out some problems with advanced mathematics knowledge, but if we can combine probabilistic thinking (the idea of distribution background and statistical replacement), we can greatly simplify the calculation and give answers skillfully.
Suggestions on reviewing probability theory and mathematical statistics of in-service graduate students in beijing university of chemical technology? The core of probability theory and mathematical statistics is relatively fixed. It is suggested that students grasp the core thread from the real questions over the years. After class, take the real questions over the years to test the learning effect. If the real problem can be solved smoothly, combined with some simulated test papers to broaden our thinking, we will certainly learn well and get full marks!
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