After experiencing the abuse of Markov chains and stable random processes, I suddenly understood the idea of probability problem-solving. In fact, it is to first analyze whether the "basic scene" is continuous or discrete, and consider probability density for continuous and probability for discrete; The distribution function uses the probability distribution function;
Then, based on the basic scenario, we will analyze the mathematical characteristics, expectation, variance, mean, or covariate, or a more complex variance function, mean function, autocorrelation function, correlation covariance function, etc.
The last step is to verify. If the first step is a hypothesis, then it is necessary to test whether H0, H1 support the hypothesis.
The rest is your scene analysis ability and mastery of mathematical tools (mathematical features).