Qingcheng, a county with an area of ​​nearly 1,300 square kilometers and a population of only about 240,000, can be said to be vast and sparsely populated.

The reason for this is that Qingcheng is located in the mountainous area of ​​​​Western Fujian. The terrain is low in the north, south, high and middle. It is the juncture of the three mountain ranges of Daiyun Mountain, Tortoise Mountain and Bopingling. It is normal for the altitude to be 700 to 800 meters, that is, the altitude is over 1,000 meters.

There are many too.

Such mountainous areas have a relatively small population. After all, people prefer to live in coastal cities such as Shuixian City, Ludao, and Licheng.

However, thanks to the Jiulong River Beixi flowing through it, the climate in Qingcheng is still very pleasant, with an average annual precipitation of about 1,300 mm and an average annual temperature of 20°C.

The large area and small population also have an advantage, that is, there are only two high schools in the entire Zhangping, namely Qingcheng No. 1 Middle School and Qingcheng No. 2 Middle School. This results in the competition in Qingcheng No. 1 Middle School not being as exaggerated as in coastal counties.

Competition to the extreme.

Liu Yichen had some understanding. There is Jinpu County in Shuixian City, the next door city. Its area is similar to Qingcheng, but its population is 810,000. The number of students in each class of Jinpu No. 1 Middle School is about the same as that of Qingcheng No. 1 Middle School. This means that Jinpu County

For students who want to enter Jinpu No. 1 Middle School, the difficulty is about three times that of Qingcheng students, which is much crueler.

The weeds in the half-acre field belonging to Class 8, Grade 1, are being eliminated at a speed visible to the naked eye thanks to the work of 55 students from Class 8.

As for the head teacher and other subject teachers, they held their hands on their chests, walked around leisurely, chatted in low voices, and looked at the students from time to time, so that the students felt that someone was supervising them anytime and anywhere, and they did not dare to overdo it.

Fishing.

Liu Yichen pulled the grass for a while, and was sweating profusely. He secretly cursed the school as a bastard, squeezing free labor. If he had the ability, he would open up the place, plant tomatoes, vegetables, sugar cane, etc., and then wait for the harvest to give it to them.

Let them take the fruits of their labor home to show off to their parents. Repeatedly pulling weeds every year is nothing more than labor.

Think about the school ten years from now. It will look like a comprehensive development of moral, intellectual, physical, artistic and labor. Students work, and then during the harvest season, they will go home excitedly with cabbage, tomatoes, and sugar cane on their shoulders. Even in college,

Universities with lakes drain the lake water every year to catch fish. Not only do they have a fish feast, but they also get fish and shrimp. This is awesome.

At noon in the cafeteria, Liu Yichen ate twice as much rice as usual and gnawed on a large chicken leg before burping with satisfaction, cleaning the lunch box, drying it with paper towels and putting it in his schoolbag, and then walked a little heavy

Walking towards the library at a fast pace.

The 5-kilometer jog yesterday afternoon was not the most painful yesterday. What was most painful today was the accumulation of lactic acid fermentation. Even though he had taken certain measures to alleviate it, he was still sore to the point of death. He felt sore even when he gritted his teeth.

With a strong will, Liu Yichen walked to the library in 5 minutes and found a quiet corner. He picked up the exercise book for High School Mathematics Compulsory Course 1. This exercise book contains a simple summary of the textbook content and important formulas.

, the others are questions. The content of the questions covers knowledge points, and many have extensions and expansions. They are used to help students consolidate their knowledge.

Sometimes when teachers assign homework, they will also directly assign a certain question in the exercise book.

Liu Yichen wrote in the exercise book: Liu Yichen, Grade 18, Qingcheng No. 1 Middle School.

Then he opened the exercise book. He did not look at the summary of the previous knowledge points, but directly solved the questions. Only when he encountered questions that he did not know, Liu Yichen would go back to look at the knowledge points and understand them again, so that he could have a higher level.

With high efficiency, you can also discover knowledge points that you have not mastered.

Liu Yichen, immersed in the sea of ​​questions, completely forgot about external objects, as if he was the only book in the world. His eyes only saw the sea of ​​questions, and he was swimming in the sea of ​​questions.

This kind of happiness is beyond the comprehension of ordinary people!

Time passed by, and before he knew it, he had already solved one-third of the questions. The operation was as fast as a tiger's and went smoothly, as if he had never encountered a bottleneck, whether it was about collections or one yuan.

Quadratic functions were like weak chickens in front of Liu Yichen, falling apart and becoming victims of his writings, becoming sacrifices on his way forward.

Suddenly, when Liu Yichen was about to continue working on a comprehensive operational problem, he felt something poked his arm.

Liu Yichen looked sideways and saw a delicate-looking girl wearing round glasses and short hair. She was holding a pen in her hand and looking at him sheepishly.

"Classmate, I'm sorry to disturb you...can I ask you a question?" The short-haired girl was very shy and blushed when she spoke. She lowered her head and did not dare to look at Liu Yichen.

80 points!

Liu Yichen secretly gave this short-haired girl a score for her appearance. Although she has a short haircut and no makeup, she has good facial features, fair skin and tender skin. She is a beauty at first glance. If she has another beauty look, start shaking.

During the live broadcast, Ge Dazhuang's popularity is probably not even comparable to that of Ge Dazhuang. I don't know how many animals will call me "wife" and then give me a reward, just hoping that she will look at me one more time.

Beautiful women always get preferential treatment.

Liu Yichen nodded generously and said, "No problem, just ask!"

At this time, Liu Yichen was feeling narcissistic in his heart. There were only fifty to fifty students reading in the library. Instead of asking anyone else, this girl asked herself.

The only reason is that I am more handsome than others!

Liu Yichen likes to communicate with people who are discerning and proactive. As for giving lectures, it doesn't matter whether he knows it or not.

"Thank you." After whispering thank you, the girl moved the topic in front of Liu Yichen and thoughtfully handed over a pen and scratch paper.

It smells so good!

Liu Yichen smelled the faint girly fragrance, and the pores all over his body opened, and he praised it secretly.

Then he was not polite. After taking the pen and paper, he looked at the question:

"For a certain qualification exam, each candidate has up to three exam opportunities within a year. Once he passes a certain exam, he can receive the qualification certificate and no longer take part in future exams. Otherwise, he will continue to take exams until all three opportunities are used up.

.Li Ming decides to take the exam. If the probability of passing each exam he takes is 0.6, 0.7, 0.8, and whether he passes each exam is independent of each other, try to find: (1) The distribution of the number of exams x that Li Ming takes in a year

Column; (2) The probability that Li Ming will receive the qualification certificate within one year."

Liu Yichen pondered for a moment.

"This is a question about discrete random variables and their distribution." Liu Yichen said, and then looked at the short-haired girl with some surprise.

Discrete random variables and their distributions are part of random variables and their distributions, but they are not part of high school mathematics compulsory course 1, but high school mathematics compulsory course 3.

Looking at the textbook again, this textbook is very new. It was obviously just issued, which means that the short-haired girl is not a classmate in the first year of high school, but a senior in the second year of high school!

Thinking again, how could this group of rookie high school students who had not yet integrated into the learning atmosphere of Qingcheng No. 1 Middle School come to the library to study at this time? Their hearts were still wandering.

Sure enough, I am not the only one who works hard. A little girl has just started the first semester of her sophomore year in high school, and she has already taught herself the seventh chapter of High School Mathematics Compulsory Course 3.

What reason do you have for not working harder!?

"Beautiful classmate, from the question we can see that Li Ming has up to three exam opportunities in a year, which means that the number of exams is 1, 2, and 3, and its corresponding distribution column is p(x=1)=0.6,

p(x=2)=(1-0.6)*0.7=0.28,p(x=1)=0.6,p(x=3)=(1-0.6)*(1-0.7)=0.12. So the number of exams

The distribution column of x should be as follows..."

Liu Yichen wrote down the steps to solve the problem on the paper with the pen in his hand, and then listed the distribution column of the number of exams x.

"As for the second question, what is the probability that Li Ming will receive the qualification certificate within one year? We can look at the problem the other way around. What is the probability that Li Ming will not receive the qualification certificate within one year? From this perspective,

The probability of not receiving the qualification certificate within one year should be = (1-0.6) (1-0.7) (1-0.8) = 0.024, which means that the probability of Li Ming receiving the qualification certificate within one year = 1-0.024 = 0.976!"

In less than a minute, Liu Yichen wrote down the ideas and steps for solving the second question, and then came up with the correct answer.

"Classmate, you are so awesome~~" The short-haired girl looked at Liu Yichen with some admiration: "I am in the second grade of high school (10). My name is Feng Lin. Which class are you in the second grade of high school, or are you a senior in the third grade of high school!?"

"Um...Sister Feng Lin, my name is Liu Yichen, and I'm in Class 8, Grade 1." Liu Yichen said with some embarrassment.

Grade 1 (8) class?

Feng Lin was stunned!

No way? Did I hear it correctly?

A freshman in high school, understands discrete random variables and their distribution series?

"Beautiful senior? Beautiful senior?" Liu Yichen waved his hand, feeling helpless towards the cute Feng Lin.

Although you are handsome, it wouldn't be nice if you lose focus in front of yourself, right?

"I'm sorry, I'm sorry!" Feng Lin reacted and her face turned redder.

"Junior, you are so amazing. You are just a freshman in high school and you can solve such a difficult problem!" Feng Lin said.

"Is it difficult? It's okay, the difficulty is just average~~" Liu Yichen said with some embarrassment.

So irritating!

Is this called average difficulty?

Feng Lin was hit hard again. As a good student, Feng Lin studied very seriously. As soon as she got the new textbook, she took the initiative to study by herself. Moreover, her math score was not bad. Liu Yichen couldn't solve the questions she couldn't understand.

Solve the problem in three minutes.

Such a difficult question turned out to be average in difficulty!

Junior, didn’t anyone tell you that straight men can’t get girlfriends in school?

Sure enough, men with science majors are a group of ungraceful men who deserve to be single and spend time in the library alone!

At this time, Feng Lin finally understood why those men in science and engineering were all single. They were single entirely based on their ability.

Feng Lin, who was a little hurt, silently left with a pen and paper and returned to her study position. She had already made a cross in her heart for a certain straight man.
Chapter completed!