"Yes, Bayes' theorem, that's how I understand it. "Xia Lu has never underestimated Zhang Kai's mathematical strength, Zhang Kai is right, it's just a Bayesian theorem, why hide it for fear that others will steal it?

It is the basic quality of a college student to be tolerant and to listen, to unite classmates and to respect teachers.

The two came to the cafeteria, and in order to show their sincerity, Xia Lu invited Zhang Kai to breakfast.

The breakfast in Xia Lu is very classic, fritters and soy milk.

Zhang Kai's breakfast is very real, with meat and milk.

Zhang Kai was eating the meat bun, and suddenly asked: "Xia Lu, what kind of meat did you say was in the meat bun?"

Xia Lu replied without thinking: "Pork." ”

"Is pork or rabbit more expensive?" Zhang Kai asked again.

"This ......" Xia Lu was unable to answer for a while, he said: "Rabbit is so cute, I never eat rabbit meat, so I don't know the price of rabbit meat, but I feel that rabbit meat will be a little more expensive." ”

Zhang Kai said while nibbling on the meat sandwich: "On the contrary, I think pork is more expensive. Suppose I have a pound of rabbit meat and you have a pound of pork, we immediately go to the poultry market and ask about the price of rabbit meat and pork, if the pork is expensive, your pork belongs to me, if the rabbit meat is expensive, my rabbit meat belongs to you. Would you like to play this game with me?"

Xia Lu thought for a while and said: "The setting of this game is not fair, if I lose, I will lose the cheap pork to you." And if I win, I get more expensive rabbit meat. So I took advantage. ”

Zhang Kai smiled meaningfully: "In the same way, I will also feel that I have taken advantage of it, because I think pork is more expensive." ”

Xia Lu was stunned, and then laughed, and there was some self-blame in the laughter: "It's interesting and interesting, whoever thinks that he has taken advantage of it, in fact, who suffers more." Zhang Kai, you have taught me a new mathematical theorem, I was wrong, I was really wrong, from now on, I will share all the information I think is valuable with you without reservation. ”

"Do what you say, Xia Lu. Zhang Kai wiped out the meat bun and drank milk to moisten his throat.

Xia Lu tore the fritters and soaked them in soy milk, and he said sincerely: "Zhang Kai, your talent in mathematics is so high, you should really major in mathematics, and the Fields Medal in ten years is waiting for you to win." Biology is a pit, burying science students, I advise you to think carefully about your professional direction. ”

Zhang Kai shook his head and said: "My ambition has been decided, I only want to focus on biotechnology, which is something I decided when I cleared the Resident Evil level in the first grade of primary school." When we do biological experiments next semester, we are not allowed to take apart the combination. ”

"Okay. Xia Lu finished breakfast, and then went back to the bedroom with Zhang Kai to sleep.

The young man slept for a few hours enough to regain his energy and strength, and at four o'clock in the afternoon, the math exam was held as scheduled.

Xia Lu, who was resurrected with full blood, got the math test paper and scanned the questions first.

Professor Yu's style of questioning is really the same as the legend, he never comes up with multiple-choice questions.

There are only two types of questions on the paper, fill-in-the-blank and answer-and-answer questions.

Fill-in-the-blank questions are 40 points, and there are eight questions in total, all of which are regular high math questions, such as Taylor's formula, median value theorem, Lobida's rule, and so on.

These 40-point fill-in-the-blank questions are equivalent to Professor Yu's free gifts, and students in ordinary classes can get at least 30 points or even all 40 points if they answer the questions.

There are three questions to answer, the first question is 15 points, and the limit is solved. The second question is also 15 points, and it is a full differential.

Extreme and calculus are all basic skills, and Xia Lu quickly completed the first 70 points.

The last question of 30 marks is the main event, and the question of this question is:

"Let's say you're a boxing broker and your job is to invest in boxers with potential, and you can only make one investment in seven years, invest in one boxer. At the same time, the boxer also has the right to choose whether or not to work with you. ”

"Boxer investment projects with an annual return of 20% are available every year. For boxer investment projects with an annual return of 60%, the probability of appearing and not appearing every year is 50%:50%. ”

"In what year did you invest in a boxer to maximize your returns?" and write down the derivation process and the answer you think is correct. ”

"Attached:

Bayes' theorem: P(Bi∣A) = P(Bi)P(A∣Bi)/∑nj = 1P(Bj)P(A∣Bj). Tip: Use known past experience to predict unknown probabilities in the future.

Nash Balance: If the combination of strategies of two players in the game constitutes their own dominant strategy, then this combination is defined as Nash balance, and each player's balance strategy is to achieve the maximum value of their expected returns.

Pareto optimal: If both parties agree on something, both parties benefit. If either person objects, neither party benefits. ”

Professor Yu's routine is so varied that the students thought he would come up with a marriage proposal, but he ended up with a boxer investment question. The number of years set in the title is also 7 years, and the protagonist has been changed from a young man who proposes marriage to a boxing agent.

Xia Lu smiled, the question changed, but the mathematical principles involved remained the same.

The key to solving the problem is the application of Bayes' theorem.

Nash equilibrium and Pareto optimality are auxiliary properties, and it is enough to understand their core ideas, without having to delve into the whole set of theoretical principles behind them. If you really want to study John Nash's theory and Pareto's system thoroughly, you should be able to go to graduate school of economics.

An all-nighter didn't stay up in vain, Xia Lu wrote:

E{dN(t)∣Z，D≥t，v}=dμ0(te^β0X，v)+γ0Wdt……

Stabilize the situation with a bunch of formulas, which is a math problem and not an essay problem after all.

The mathematical language contained in mathematical formulas describes the literal content.

If there is no high-quality boxer with a return of 60% until the seventh year, then the boxing agent can only invest in an ordinary boxer with a return of 20%, because it is the last chance. This is the lowest return option and can only get 20% of the income for one year.

If you invest in an ordinary boxer in the sixth year, then the boxing agent will receive a 20% gain for two years in a row.

According to this reversal, in which year can the boxing agent make a move in order to get the most profit?

The variable, or bait, is a quality boxer with a random 60% gain.

In what year is a good boxer most likely to show up?

With Xia Lu's current level of mathematics, he can't calculate the exact year of the appearance of a good boxer and the corresponding probability.

Xia Lu believed that no one in the class could complete the above accurate calculations.

This is something that only a math god can do.

For a first-year student like Xia Lu, there is no need to make accurate calculations, just estimates.

This should also be Professor Yu's original intention.

So Xia Lu began to estimate:

∑ni=1∫{Zi-Z(t；α}dNi(t)=0……

Based on Bayes' theorem, Nash equilibrium, and Pareto optimality, Xia Lu made a basic probability convergence operation, and his ideas gradually became clear, and the results of the mathematical major axis subproblem became clearer and clearer.