1. Conditional probability and independence: Conditional probability refers to the probability that another event will occur when one event is known. Independence means that two events do not affect each other. These two concepts are very important in practical application, but they are not easy to understand.
2. Random variable and its distribution: Random variable is an important concept in probability theory, which can be used to describe the numerical characteristics of random phenomena. The distribution of random variables describes the possibility of random variables. This part involves many formulas and theorems and needs a lot of time to understand and remember.
3. Law of large numbers and central limit theorem: These two theorems are very important theorems in probability theory, which describe the regularity of random phenomena under certain conditions. However, the process of proving these two theorems is very complicated and requires a strong mathematical foundation to understand.
4. Parameter estimation and hypothesis testing: Parameter estimation and hypothesis testing are commonly used methods in statistics, which can be used to estimate unknown parameters or test hypotheses. This part involves many statistics and distribution functions and needs a lot of time to learn and master.
In a word, probability theory is a very profound subject, involving many abstract concepts and complex calculations. Learning this subject well requires a solid mathematical foundation and strong logical thinking ability.