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What's the difference between probability theory of mathematics department and mathematical statistics and science and engineering?
Probability theory and mathematical statistics in the department of mathematics pay more attention to theory, theorem proof and some probability properties. For example, the limit theory of probability cannot be found in general science and engineering textbooks. For example, the theorem of large numbers and the central limit theorem, the mathematics department requires to prove convergence in probability. In mathematical statistics, the department of mathematics requires to prove the commonly used statistical distribution. These contents are difficult and theoretical, so it is not easy for ordinary students to learn by themselves.