Following this series in 2024 and its still gold♥.

That's basically 3 different games where the car doesn't move and you pick a different door each game. Any time you simulate as if player's already picked the car or know where the car is, the simulation or explanation is invalid. Player picks a door, that door has a 1/3 probability to contain the car. So if he opens that door, he has a 1/3 probability to get the car. Monty's action doesn't change that. So if he stays, he can open that door and has a 1/3 probability to get the car. If he switches, that other door he can now open also only contains 1/3 probability of him getting the car. Player has a equal probability to get the car no matter which door he opens. This will go down as the biggest hoax in mathematics history. You guys never should have doubted Paul Erdos.

Horrible explanation. Not clear where the probability comes from. Zero becomes 1/8 without showing how

In this lesson very obscure explanation

I don't understand the part P (NA, B). Why not A and B we have 1/3?? Not A are only two options, Not A first option is B, Not A second option is door/room 3. Shouldn't it be then 1/2? P(NA, B) = 1/2x0 in the case when the car in the B and 1/2x1(in the case when the car behind the 3rd door, so it is only 1 option), so P(NA,B) = 1/2, I am so confused

Will you please show how to set up both integrals with the limits of integration.

caar..

Good stuff! I love it !

very confusing video

Dude, you sure this is your channel?

Options............ A, B, C = 3/3 Pick...................A = 1/3 ... B, C = 2/3 Goat revealed...B = 0/3 ... C = 2/3

Thank you so much

We are deriving g1 from sample Momen equation I.e sum of Xi/n = uhat then g1 should be zero and so does g2, g3, g4

Hahaha, spent a whole week scratching my head as to what "conjugate" meant after my professor's roundabout wishy-washy definition, only for it to be easily explained in like 2 seconds

These videos are underrated.

wrong

since you can't possibly choose the door that the host reveals which is always a goat, you start with 1/2

Sorry for waiting for 10 years But your notation for gamma distribution is wrong because you interpreted the order of parameters incorrectly😊

I didn't understand why the probability of not A is 1/3. If the probability of A is 1/3, shouldn't the probability of not A being 2/3? Could someone help explain this? Thanks!

Great stuff, but why is the impedance of free space (a vacuum) 336.7 Ohms?

A small note (given the wonderful videos) . . . this should be no 28 . . no?

For those a bit confused by the problem, I'll rewrite it here with more words - There is two tribe labelled 0 and 1. The 0 and 1 are not probability but just names. - We know with perfect accuracy if the individual are healthy or not. This is not a case were we have an imperfect test and it is possible that an individual has the disease but test negatively. In this universe, either someone is lying on the bed dying, or is running around in the jungle, with no in between. Ox Educ confusingly used the term "asymptomatic", but then say they are healthy. The rest of the problem assume we know they are healthy. - Theta = 1 does not mean that all the members are sick, it just mean "We sampled the individual from tribe 1, the one where some member are sicks" - Our model of the probability of an individual being sick is the function f, and it depend on the tribe we sample from. In tribe 0 no one is sick. so f(0) = 0 . In tribe 1, the infected tribe, half the member are sick, the other half is in good health, so f(1) = 1/2. Remember that 0 and 1 in the function parameter are just the tribe label, and not really a number. - Since all the individual we picked are healthy, we cannot be sure which tribe we picked them from. If any of them was sick, then we would have instantly knew that it was tribe 1, because it is the only on that has sick members. But with our current data, either we sampled from tribe 0 that has only healthy individual, or we sampled from tribe 1, and by chance, only picked from the healthy half of the tribe. So P(data|theta = 1,model) is 1/8, since we picked three individual, and our model say we have 1/2 chance for each individual for them to be healthy if we sample them from tribe 1

thank you for going through a complete example from scratch. helped a lot.

The videos are good information and knowledge wise but kinda boring. I loose my focus every now and then.

i needed this so much! when i started my horribly organized probability theory class i needed simple and clear explanations to all the terms that were thrown in . well i didn't get it then but luckily you exist ! wishing you all the best !

good

Do you know how complex is the induction proof?

At four minutes and 23 seconds, you started to talk about geometrically defining dual vectors. I got really excited because I was sure you were going to talk about parallel projection versus perpendicular projection which describe contra variant components and covariant components a.k.a. dual basis vectors, respectively. Is there a connection between one forms and the perpendicular projection of vectors components called dual basis vectors ?

Brutal video

where does the values of 0.25 and 0.4 comes from?

This is a triumph of excellent teaching. Thank you.

Cool video! I finaly understood it! There are not so much about this theme in the web... thank you!

I'd like to mention that we can go beyond the Monty Hall problem and touche on a fundamental issue in probability and statistics: the comparability of events with different sample spaces or magnitudes. 1. A first event with a magnitude of 3 (three doors) 2. A second event with a magnitude of 2 (two doors) While a great introduction into probability, the Monty Hall Problem only works if one accepts the comparison of two events of different magnitudes as logical. To dismiss people who cannot agree with this comparison as they do not get it is a problem if you ask me. I see the importance of highlighting both ways of thinking. In many contexts, comparing probabilities from events with different magnitudes or sample spaces is indeed problematic or even meaningless. For example, to provide another example of fundamentally different events: Comparing the probability of rolling a 6 on a die (1/6) with the probability of flipping heads on a coin (1/2) doesn't make much sense in isolation. In more complex scenarios, like comparing stock performance across different markets or time frames, not accounting for differences in magnitude can lead to serious misunderstandings. Additionally, people think if your initial choice was the car (which happens 1/3 of the time), then switching would be the wrong move. In this case, the host's reveal of a goat door doesn't help you at all. You've already won, and switching would make you lose. If one accepts the comparison of two events of different magnitudes, the Monty Hall strategy isn't about "always switch" but rather "switch because it's more likely you initially picked a goat." The host's reveal doesn't create new winning chances. The host doesn't change the fact that you probably (2/3 chance) guessed wrong at first.

Lovely video Ben! As usual.

How could you say that theta is fixed when you integrate over it’s “different” values in 1:06

Thank you very much Ox, your class is extremely outstanding and great!

How dare I found this now.. Amazing works !

I am confused by p(a,b)= 1/3 x 1/2. Does this assume A and B are independent? If they are independent, p(a|b)=p(a); no need to go through all the rest of the derivation steps.

why did you write P(\theta) that way, isn't that the density function of \theta and not the actual probability ?

First day on Bayesian statistics. Lets go!

This was useful for me in understanding why with entropy and cross entropy with KL Divergence the Cross entropy will always be greater than the entropy (you have to flip the inequality though because the function in question is a -log which is concave

Can't believe I'm learning what people learned 9yrs ago and I'm surprised what are they doing now 😳

2:26

1:48

0:13 0:14 0:14

fantastic! absolutely fantastic explanation!

Would this also imply the reverse is true for a concave function? I.e., g(E(x)) > E[g(x)] ?

Stretching is dual to squeezing -- forces are dual. The Ricci tensor (positive curvature, matter) is dual to the Weyl tensor (negative curvature, vacuum). "Always two there are" -- Yoda. The Ricci tensor is the symmetric projection of the Riemann curvature tensor. The Weyl tensor is the anti-symmetric projection of the Riemann curvature tensor. Symmetry (Bosons) is dual to anti-symmetry (Fermions). Covariant is dual to contravariant -- dual basis.

Is an average football fan better educated (more sensitive to other cultures?), than average mathematician: kzbin.info/www/bejne/aaLUpKOLiN2fgJI

Where did the N choose X part go though?