In what areas is the knowledge of mathematical statistics applied?

This question is too broad, and I don’t know how to answer it. I am a major in applied mathematics, not statistics. Let me give you my understanding. Whether it is probability or statistics, they all study random phenomena in life. Strictly speaking, everything is random, so in a broad sense, probability and statistics can be applied to anything. Probability theory originated from insurance problems or gambling problems. This was also the earliest application. Later, probability theory had an axiomatic definition, and mathematical statistics also became an independent branch. Its applications are too wide. Just to name a few, such as buying lottery tickets, playing cards, and playing mahjong, the essence is to maximize your expectations. Take playing mahjong as an example. Why should you try to play white, white, or 1, 9 in the southeast, northwest, and middle? Because the probability of these cards forming a valid card (3 of the same or 3 in a row) is relatively small. Let’s talk about mahjong’s reward settings. Why do different Hufa have different rewards? The essence is also probability. The lower the probability of a trick, the higher the reward. In fact, basically the scoring system of chess and card games has this idea~

There are more mathematical statistics, and there are more points. There are many detailed subjects. Needless to say, the National Bureau of Statistics is really good at it, right?

In short, this question is a bit broad and difficult to explain clearly. The level is limited and it is embarrassing