शैडोइंग अभ्यास: Mathematical Statistics and the Theory of Probability in Casinos - वीडियो के साथ अंग्रेजी बोलना सीखें

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

शैडोइंग तकनीक क्या है?

शैडोइंग (Shadowing) एक विज्ञान-समर्थित भाषा सीखने की तकनीक है जो मूल रूप से पेशेवर दुभाषिया प्रशिक्षण के लिए विकसित की गई थी। विधि सरल लेकिन शक्तिशाली है: आप मूल अंग्रेज़ी ऑडियो सुनते हैं और तुरंत इसे ज़ोर से दोहराते हैं — जैसे वक्ता की छाया 1-2 सेकंड की देरी से। शोध से पता चलता है कि यह उच्चारण सटीकता, स्वर, लय, जुड़ी हुई ध्वनियाँ, सुनने की समझ और बोलने की प्रवाहशीलता में काफ़ी सुधार करता है।

शैडोइंग अभ्यास: Mathematical Statistics and the Theory of Probability in Casinos - वीडियो के साथ अंग्रेजी बोलना सीखें

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शैडोइंग तकनीक क्या है?