Taking Probability Theory and Mathematical Statistics (Higher Education Press, Fourth Edition) edited by Sheng Zhi and others as an example, the basic requirement for postgraduate entrance examination is the parameter hypothesis test in the first seven chapters and the eighth chapter. Different schools and majors have different emphasis or extension on teaching content because of different hours.
If the foundation of advanced mathematics (or calculus) is not very solid, you'd better do a good job of reviewing before class (if it's too late, at least spread the review to all chapters), otherwise calculus will become a stumbling block for you to learn probability statistics. In fact, all the knowledge and operations used in calculus are very basic. The following is the preparatory knowledge required for each chapter of probability statistics for your reference.
The first chapter, "Basic Concepts of Probability Theory", uses the relations and operations of sets and the knowledge of permutation and combination.
The second chapter "Random Variables and Their Distribution" makes use of the basic operations of definite integral (including generalized integral on infinite interval) and the additivity of definite integral to integral interval, especially when the integrand function is piecewise function.
The fourth chapter, "Digital Characteristics of Random Variables", uses the basic operations of summation of several series, definite integral (including generalized integral on infinite interval) and double integral. When talking about n-dimensional random variables, we will use the notation of matrix operation in linear algebra, but it is only mentioned slightly that this is to prepare for further study in the future and is generally not the focus of the exam.
The fifth chapter "Law of Large Numbers and Central Limit Theorem" uses the concept of limit to define the convergence of random variable sequence and function sequence with the help of sequence limit.
Chapter VI "Samples and Sample Distribution" basically does not require knowledge of advanced mathematics (or calculus).
In Chapter 7 "Parameter Estimation", the moment estimation part uses the summation and definite integral of several series (including the generalized integral on infinite interval), and the maximum likelihood estimation part uses the properties of logarithmic operation, derivative (including partial derivative) and basic operation for finding extreme points.
Chapter 8 "Hypothesis test" basically does not require knowledge of advanced mathematics (or calculus).
This course should not only have the knowledge base of elementary mathematics and calculus, but also have the knowledge points of its own chapters. For example, learning the second chapter "Random Variables and Their Distribution" will be of great help to master many concepts or basic relationships in the third chapter "Multidimensional Random Variables and Their Distribution". In calculation, as long as you pass the third chapter, you won't find the following chapters difficult to learn.
In short, it is very important to grasp the initiative in the primary stage of learning probability theory and mathematical statistics. After getting started smoothly, with the deepening of your study, you will gradually find that stochastic mathematics is a new world full of special charm!