Hammer of Technology

nonexistent!

No money!

……

"If you want to be so good, help me read this question." Xu Mo unceremoniously handed over a piece of A4 paper with the question printed.

Ning Wei took it over and took a look.

"There are a total of N machine tools in a workshop. Because of the need to change tools and measure, the machine tools need to work sometimes and stop sometimes. Suppose a machine tool that is working at time t, the probability of stopping working at t+△t is μ△t+O(△ t), then suppose a machine tool that does not work at time t, the probability of starting to work at t+△t is λ△t+O(△t), and the working conditions of each machine tool are relatively independent. Use X(t) to represent t The number of machine tools that are working at all times.”

"Prove: a, {X(t), t≥0} is a process of a homogeneous Markov chain;"

"b. Find its stationary distribution;"

"c. Especially when N=10, λ=60, and μ=30, find the probability that at most three machines will not work in the steady state."

……

After reading this topic, Ning Wei's first feeling is speechless.

Funny!

When does counting to three require candidates to kill the process?

But the next moment, Ning Wei was shocked.

Because he hadn't had time to start thinking about where to start with this problem, a complete problem-solving process had automatically emerged in his mind.

Very concise, complete, and includes an answer to the last question.

The probability of at most three not working is 0.599.

Not only that, but there are also many related concepts that he doesn't understand, such as Markov chains, in his mind.

It even extended the related machine learning algorithms, Markov random field and Markov decision.

This feeling is familiar...

------------

005 I would like to be single for ten more years

Xu Mo looked at Ning Wei triumphantly.

That's right, she is in Corningwei.

It's not that Ning Wei did something wrong, but that Xu Ruixuan is dishonest!

In fact, there is another version of the ins and outs of the whole incident, just to take care of Xu Ruixuan's face, the two girls didn't talk about it.

The first meeting was actually only three people.

Xu Mo took his best friend to the self-study with Xu Ruixuan in the general map, and soon discovered that it was a parallel import.

Xu Ruixuan can only admit that he actually discussed some of the problems with other students. .

Everyone made an appointment to meet the classmate who is good at mathematics the next day.

After Xu Ruixuan returned to the dormitory, he thought carefully for a long time and felt that he still couldn't drag Ning Wei to meet Xu Mo.

If anyone in the dormitory threatened him in terms of appearance, it would be Ning Wei.

Tall, thin, handsome, with good grades...

Before he could establish a relationship with Xu Mo, Xu Ruixuan felt that Ning Wei could not be directly involved.

Although everyone in the dormitory has a good relationship, who is not selfish when it comes to future happiness?

So he called Liu Cong.

Who made Liu Cong, nicknamed Fat Wolf, the fattest in the room?And I have a lot of pimples on my face.

Anyway, Liu Cong's grades are better than his.Maybe it was muddled?

Unfortunately, they failed again...

That's why this meeting happened.

Now Ningwei's performance seems to be a possibility of parallel imports.

After all, the topic is so long, so don't worry about it for a few minutes, right?

How did she know that Ning Wei's heart was already shocked beyond measure.

If Ning Wei was not sure if there was any abnormality in his body when he was in the dormitory, then now he is sure that there is a high probability that there is something wrong with his brain.

There is a saying that there is often only a thin line between a genius and a madman.

Ning Wei felt that he should be going crazy.

……

"Have any ideas?"

Xu Mo's question awakened Ning Wei from his own world.

First, he raised his head and glanced at Xu Ruixuan who was winking at him, then nodded at the girl opposite.

"It's solved."

"what?"

Xu Mo was stunned for a moment, apparently he didn't expect Ning Wei to say this sentence, how did he explain it?Calculating silently in your heart?

"First prove a, here we have to divide it into two steps, first prove that it is a Markov process, and then prove that it is a homogeneous Markov process."

"Because a machine tool that is working at time t, the probability that it will stop working at time t+△t is μ△t+O(△t); a machine tool that is not working at time t, the probability that it will start working at time t+△t is λ△t+O(△t); these results have nothing to do with the previous t and are only related to △t. The title has shown that the machine tool is independent of working conditions, so it can be seen that this is a Markov process."

"The next step is the second step. It can be deduced from the conditions: Pij(△t)=P{X(t+△t)=j | X(t)=i}"

"It can be obtained from this: (Ni) λ△t+O(△t), j=i+1, that is, the Ni station is broken, and another one is good;"

"iμ△t+O(△t), j=i-1, that is, one of the good i units is broken;"

"1-(Ni)λ△t-iμ△t+O(△t), i=j, that is, a good one is bad, and a bad one is good;"

"O(△t), | ij |>1, that is, it is impossible to have two good and bad machines at the same time."

"It can be seen that the transition probability from t to t+△t is only related to △t and has nothing to do with t, so this Markov chain process is homogeneous."

"Then the second question is to find a stable distribution. From the above conditions, we can know..."

Ning Wei entered the problem-solving state, and began to write and draw on the paper.

In fact, Ning Wei is not very good at giving lectures, but he has the most detailed problem-solving process in his mind, so he only needs to transcribe the things in his brain step by step.

As for whether the beauty next to her could understand, Ning Wei didn't really care much.

“由以上的推论，我们可以得出P｛至多三台不工作｝=P｛7≤X(t)≤10｝=P7+P8+P9+P10=0.599.”

"That is, when N=10, λ=60, and μ=30, the probability of at most three not working in the steady state is 0.599."

……

Xu Mo took the manuscript paper that Ning Wei answered the question with a dazed expression, and handed it to his best friend.

Ning Wei was very attentive when solving the problem, so he didn't notice that Yang Xiaohui glanced at him from time to time when he started to solve the problem.

Yang Xiaohui took the manuscript paper for answering the questions, then opened the book she was opening, and turned to the end. After careful comparison for a few minutes, she said: "All are correct, and the process of solving the questions is more detailed than the reference answers in the book."

"Haha, I just said that capable people are in our dormitory. Hey, it's not that I don't want to bring Ning Wei out. This guy is very obedient. He has to go to self-study with his girlfriend every day. It is necessary to pull him out today." Thank his girlfriend for giving him a vacation!"

Xu Ruixuan winked at Ning Wei.

Ning Wei also finally figured out why he wanted to have a girlfriend today.

He couldn't help but burst out laughing, and then fell silent.

Well, it seems that Xu Ruixuan has really taken a fancy to Xu Mo.

What he didn't know was that Luo Xiang actually wanted to speak up, but when he was solving the problem, Xu Ruixuan handed Luo Xiang a note, promising meals for a week, and Luo Xiang rebelled.

Fortunately, Ning Wei has no plans to fall in love at this time.

If he could, he would even be willing to stay single for ten years in exchange for being able to figure out what happened to him today!

Anyway, I have been single for 22 years, and I will be single for another ten years.

He also doesn't have the money and time to talk about an ordinary love recently.

Of course, I would rather not let go of the desired benefits.

"Well, Mr. Xuan, does your promise to invite me and my girlfriend Qijiu to eat barbecue with wine for a day still count?" Ning Wei asked, looking at his roommate opposite.

"Well, it counts, it must count."

"However, she said that she can't eat barbecue because she wants to lose weight recently. Why don't you convert it into treating me to meals for a week?"

"Of course it's fine!"

When Ning Wei wanted to say something, the phone vibrated.

Ning Wei picked up the phone, smiled shyly at the girl beside him, then picked up the phone and went to the corridor.

"His girlfriend?" Xu Mo asked Xu Ruixuan.

"Maybe?"

"You girls in several colleges are really strict with your boyfriend!"

"Haha, so so so!"

Yang Xiaohui next to her turned her head curiously again, and glanced at Ning Wei who was leaving.

These guys seem a little weird.

……

The call was from the instructor.

"Hey, Ning Wei, where are you now?"

"Self-study in the general map."

"Oh, come to my office now if you have time."

"Okay, I'll be there in about 10 minutes."

"Okay, don't worry, I'll wait for you."

……

Back at the desks of the two dormitories for self-study, Ning Wei said apologetically, "I'm sorry, I have something to do and I have to go first. You should study by yourself first, see you next time."

"Are you really looking for a girlfriend?" Xu Mo asked.

"Hehe..." Ning Wei laughed twice, without explaining.

"Oh, it just so happens that I have something to do, I have to go back to the dormitory, let's go together." Luo Xiang, who could no longer sit still, said.

"Okay, if you have something to do, go first, remember to return the position within an hour, or you will be pulled into the blacklist of the general plan." Xu Ruixuan said with a very knowledgable look.

------------

006 Insurance research?I am not rare anymore!

"Which girlfriend of yours is looking for you?"

"Oh, instructor!"

"I guess so."

"Why don't you stay there and go to self-study with the beauty?"

"Obviously, Xu Ruixuan and Liu Cong have a deep-rooted relationship. The meal is ready, and you suddenly have something to do. I'm really ignorant to stay there." Luo Xiang spread his hands and said.

"These two guys..." Ning Wei thought for a while, then patted Luo Xiang on the shoulder, and continued: "When a man's hormones are over-secreted, his brain is usually not very bright. So forgive them. By the way, you go back first. bedroom?"

"No, I'll accompany you to the instructor's side. Your opinion should come out. If it's unreasonable, I'll help you argue."

"Huh? Well, actually, I don't think there is any need to argue." Ning Wei was a little embarrassed.

If he had known that his body would undergo the changes today, he might not have conflicted with the admissions teacher at all.

The problem now is that he still doesn't quite know how this is going on, and how long this situation will last.

But one thing is for sure.