쉐도잉 연습: Mathematical Statistics and the Theory of Probability in Casinos - 영상으로 영어 말하기 배우기

Thanks for watching my video.

It looks like a lot of you guys want me to talk about math problems for some reason.

In case any of y'all don't know already, I went to UC Berkeley for undergrad and double majored in applied math and operations research.

I've been procrastinating making this type of video because the thing is, I know how to learn, but I don't really know how to teach.

Anyway, since I'm going to be a PhD student in operations research very soon, I might as well start practicing teaching, you know?

Oh, by the way, there are a lot of mathematical terms that I don't know the Chinese for, so this whole video is going to be in English.

Sorry about that.

I want to start with the very basics of stochastic processes, the Markov chain.

So let's think about a process that has a value in each time period

and build a probability model from one period to another.

It would be easy to assume that all of those values or random variables are independent from each other,

but most of the time that's not the case at all, and this is where the Markov chain becomes handy.

So for a Markov chain, we say that the future depends on the past only through the present,

aka the conditional distribution of the random variable in time period

n plus one given all the past distributions is the same

as the conditional distribution of time period n plus one given only period n.

So let's have an example for understanding.

Maybe gambling from the very popular movie recently.

So if the guy had know more about the market chain, I don't think he would make the same stupid decisions.

Okay, for example, say that he's playing a game

and at each play he would win a thousand dollars or lose a thousand dollars.

He would win a thousand dollars with the probability of p

and lose a thousand dollars with the probability of q which equals one minus p.

Boom!

We have a market chain.

Oh actually, let's also say that he would quit playing, I mean he has to quit playing when he goes completely broke,

like zero amount of money, or if he reaches his goal and that's like a random amount of money I guess.

And mathematically it's pretty interesting because

because it's intuitive to ask what is the chance of our guy actually reach his goal before he goes completely broke.

And I'm going to add as a formula here, I think, I don't think I can say it out loud.

But as you can see, if you set the n infinitely large and your chance of winning each play is less than one half,

then actually you're going to go broke with a probability of one, which means you're definitely going to go broke.

So the lesson is if you gamble and can't stop, you're going to go broke one day, sometime.

Yeah.

And that's it for today.

I hope it was interesting.

I just think it's kind of ironic that there are

so many fantastic apps on Bilibili posting pure study materials and most of the time no one watches them.

But for me, I almost only posted chatting slash joking videos yet so many people want to hear me talk about math.

Oh well, here you go.

Anyway, for watching please subscribe or comment down below i'll see you next time hopefully

쉐도잉이란? 영어 실력을 빠르게 키우는 과학적 방법

쉐도잉(Shadowing)은 원래 전문 통역사 훈련을 위해 개발된 언어 학습 기법으로, 다언어 학자인 Dr. Alexander Arguelles에 의해 대중화된 방법입니다. 핵심 원리는 간단하지만 매우 강력합니다: 원어민의 영어를 들으면서 1~2초의 짧은 지연으로 즉시 소리 내어 따라 말하는 것——마치 '그림자(shadow)'처럼 화자를 따라가는 것입니다. 문법 공부나 수동적인 청취와 달리, 쉐도잉은 뇌와 입 근육이 동시에 실시간으로 영어를 처리하고 재현하도록 훈련합니다. 연구에 따르면 이 방법은 발음 정확도, 억양, 리듬, 연음, 청취력, 말하기 유창성을 크게 향상시킵니다. IELTS 스피킹 준비와 자연스러운 영어 소통을 원하는 분들에게 특히 효과적입니다.

쉐도잉 연습: Mathematical Statistics and the Theory of Probability in Casinos - 영상으로 영어 말하기 배우기

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쉐도잉이란? 영어 실력을 빠르게 키우는 과학적 방법