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- Просмотров 57 365
NStatum
Добавлен 21 фев 2022
What do hats have to do with Euler's number?
This video explores the Hat-Check problem and derives the formula for the number of derangements and the probability of getting a derangement. It also covers how Euler's number can be used to simplify these formulae, and the surprising relationships that can show up in discrete mathematics.
Timestamps:
0:00 Intro
1:08 Getting an Intuition
2:52 Inclusion-Exclusion Principle
4:11 Finding Derangements
8:28 Finding Probability of a Derangement
9:02 But What Does "e" Have To Do With It?
Derangement Probability Derivation Adapted From: Discrete Mathematics and Its Applications, 7th Edition-McGraw-Hill by Kenneth Rosen pgs. 562-564
Music (in order of appearance):
- Concerto Grosso in D minor, H.143 'La Fo...
Timestamps:
0:00 Intro
1:08 Getting an Intuition
2:52 Inclusion-Exclusion Principle
4:11 Finding Derangements
8:28 Finding Probability of a Derangement
9:02 But What Does "e" Have To Do With It?
Derangement Probability Derivation Adapted From: Discrete Mathematics and Its Applications, 7th Edition-McGraw-Hill by Kenneth Rosen pgs. 562-564
Music (in order of appearance):
- Concerto Grosso in D minor, H.143 'La Fo...
Просмотров: 3 107
Видео
The German Tank Problem: How the Allies defeated the Nazis with statistics
Просмотров 4,5 тыс.Год назад
In this video, the German Tank Problem is discussed, which is how the allies defeated the Nazis with statistics during World War II. The allies received intelligence reports that there were significantly more German Panther tanks than expected, making it crucial to confirm the validity of these reports. With only two captured tanks, the statisticians used serial numbers found on almost every pi...
P-Values - Explained
Просмотров 6702 года назад
For this video, I give a very high-level overview of p-values and their use in statistics. P-values are prevalent in science and other statistical applications, unfortunately they are also commonly misinterpreted. This video aims to give a brief overview of what p-values measure, and some context surrounding their usage. Resources for Further Study: Overview of Type I & II Errors - ruclips.net/...
Counting, Probability, and the Birthday Problem
Просмотров 2,6 тыс.2 года назад
It's common to have to deal with combinatorics when solving probability questions, and in this video I explain where some of the basic formulas come from in combinatorics. I also provide a basic framework to help guide you through these often challenging problems. Timestamps: 00:00 Intro and Fundamental Counting Principle 3:00 Permutations 6:38 Combinations 11:03 Framework 12:45 Poker Cards Exa...
Underfitting & Overfitting - Explained
Просмотров 25 тыс.2 года назад
Underfitting and overfitting are some of the most common problems you encounter while constructing a statistical/machine learning model. It is therefore important to be able to recognize when either is occurring and what can be done to fix it. This is an extremely brief overview covering those topics, and, as always in machine learning, there is more to learn. Resources for Further Study: More ...
The Law of Large Numbers - Explained
Просмотров 22 тыс.2 года назад
The law of large numbers is one of the most intuitive ideas in statistics, however, often the strong and weak versions of the law can be difficult to understand. In this video, I breakdown what the definitions of both laws mean and use this as a way to introduce the concepts of convergence in probability, and the statistical meaning of a probability of zero or one. Resources for Further Study: ...
Type I & II Errors Explained in Under 3 Minutes!
Просмотров 3802 года назад
Anytime you do hypothesis testing it's important to consider the possibility of Type I and Type II errors. This video explains what those terms mean and how you can easily tell them apart in the future. Definitely spoke too fast in this video, but I'll try and bring down the pace next time. Resources for Further Study: Null hypothesis and hypothesis testing explanation: - www.thoughtco.com/null...
The birthday problem is always fun. Imagine that it was any r people. So the probability of no match then it would be P(no match)= [(365)(364) ... (365-r+1)]/365^r. Then the probability of at least 2 matches would be 1-P(no match)
Extend this so that the minimum number of people is required to have a 50% probability that at least 2 people match.
Bro please keep up with the videos your explanations are spot on!
CHEERS MATE
Awesome video. Thank you so much
mice explanation
This is NOT how the wlln and slln are differentiated, at least not how it is done in 99.99% of stochastics books.
This is a more straightforward method commonly used to solve this problem. Compare the max number found to the sum of all numbers, take the average, and double it. Then use the max of these two numbers. This method has some intuitive appeal. If the numbers are evenly distributed, the average would represent the midpoint, so doubling it could give a reasonable total estimate. I tested this out by solving a problem by estimating the highest number of houses on a street when we only knew a few of the house numbers on each street. I tested the tank method with the straightforward process, and the results were about the same.
Air superiority won the war really.
Great video. Also I hope you sign up for a diction and modulation course to help out with that pronunciation
Wow. Your explanation is incredibly concise. Thanks!
awesome
very nicely explained!
Great job at explaining the nuances of P = 0 and P = 1. As someone studying some graduate level measure theory, I much prefer your definition lol.
@5:39 the average gap = sum of all gaps/n. But no matter at what nr you start if x1=24 and x2=29, then the gap between them is 29-24 = 5 not 4. you claim the second gap has size (x2-x1-1).
Such a beautiful video and the explanation was even more beautiful! Thanks!!
The content you made is really great but your speaking too fast and it sounds as if you are swallowing your words.....its a bit teasing as we have to pause and try to understand...may be you make the pronunciation more clearer. just my opinion, I dont know if others too felt it.
this comment represents all the viewers
Great vid but can go slower for others
The video is great, it’s just one problem, the voice over. Sometimes it’s to fast, sometimes it’s unclear.
Great video, thanks
wow ! really helpful video!thanks :)
great video
very good
Very useful! Thanks
I have a question! I generally think of e as being fundamentally related to compounding growth, similarly to how pi is thought of as being fundamentally related to circles. So with that in mind, is there some important relationship between derangements and compounding growth? If there is, it isn't apparent to me.
This is what sciéΠcë is
I applaud you as a creative, but if you want a wider audience, you should make a conscious effort to speak slower and enunciate. I'm a pretty decent non-native english speaker and I had to focus way too much on deciphering what you were saying. I gave up before the end of the video.
I understand we have to round to the nearest integer because we can’t have a non integer amount of derangements. But i guess I’m a little confused on how we know for sure that rounding will result in the right answer
Don‘t worry, that was not explained in the video. The reason is simply that the approximation 1 - 1/1! + 1/2! - 1/3! - … + (-1)^n/n! = 1/e is somewhat accurate. For when you plot the alternating behaviour of this sequence, you can see that if n is even, then as the next term added is negative, you are currently above the limit, and if n is odd, you are below the limit. But the next term has only size 1/(n+1)!, which is quite small. So we know that D_n = n! (1/e + r_n), where abs(r_n) <= 1/(n+1)!, so D_n = n!/e + n! r_n, and abs(n! r_n) <= 1/(n+1). So if n \geq 2, the approximation D_n = n! / e will be accurate to within less than 1/2. As you observed, D_n is an integer, which means precisely that we can conclude D_n = round(n! / e). For n = 0, n = 1, n = 2, we can check by hand that this formula works as well.
How is this related to computer science?
But why the limit goes to infinity and not to the total number of the population? Are we assuming the population is infinite? I would think that if the population has a finite size, the mean of the sample would get the true mean of the population as the sample size approaches the population size
Why mumble
Discovered this right after taking a combinatorics-heavy discrete math class-- great vid!
Very good explanation!
(If u are a 3b1b reviewer, watch the video before reading my comment lol) I kinda got lost halfway through with all the math jargon 😅. First we were talking about hats and parties and then suddenly set intersections and permutations? The rest of the video seems to be mostly symbol manipulation and I think I'd understand it better if the actual math could be presented more closely to the context of the story. (I.e. talking about permutations of physical hats in a box, rather than items in a set)
Basically we consider the outcomes as ordered quadruples. For example, if there are 4 people, (1,2,3,4) can denote the outcome that everyone receives their hat. (2,1,3,4) denotes the outcome where the first person takes the 2nd guy's hat and the 2nd guy takes the first guy's head and the rest got their own head. So, you can consider the total number of ordering in this ordered quadruple to be 4!. Also, derangement here considers all cases where the i-th entry is NOT EQUAL to i, for all i.
Try to speak clearly bro....this is something that can help anyone around the world ..i had to slow the video and even then u weren't clear enough
loud and clear to me
perfect calming bg music choice tbh
Wow this is a very high quality video! Very informative!
It's a shame that this hasn't gone viral like other math teaching videos. It's up there with the best in terms of quality, communication and clarity. It makes harder concepts easy to digest as every good teaching video should. Good job!
I loved your videos, especially the underfitting and overfitting one. For this one I would just say it got a bit typical towards the end to understand the concept of why exactly alpha > p- value leads to reject null hypothesis. But still great work though!!
If I could give an advice, I think you should speak a little slower for the non-fluent English speakers. Other than that, good video!
well made video. thank you for helping me with stats 🙏
Nice video and well explained. However it is so difficult to understand you. So fast and not very clear :(
Only good for people that already know the content. For everybody else it is too fast not very well explained. Also you speak so fast, that I had the repeat some parts of the video up to four times to understand what you were saying.
Beautiful video! (even though I have not understood! xD)
Subscribed
Damn thanks, you really helped!
Subbed. Awesome content!
ᵖʳᵒᵐᵒˢᵐ 🙋
0:01, please try to speak more clearly. I listened twice and have no idea what you said.
Need the Nstatum soda pls
what softwares do you use for these videos? also good job!
Thanks! And I use a mix of After Effects and Manim which is a Python Package