"Throwing away information is the only way to fit the complexity of the world into our brain. The art comes in keeping the most important information." 2:16
That moment (ha!) when you've been blundering through 5 years of statistics classes and you finally understand what a moment actually is. This was a super clear video and I liked the airport example. btw the "(something I can't understand)" in the subtitles at 9:04 is "rises to a peak in the middle".
He is simply saying that the variance of the distribution is largest when p = 0.5. Since the variance of the distribution , V, equals p(1-p) = p - p^2, take the first derivative of this function: dV/dp = 1-2p. Setting it equal to zero gives its optimum: p = 0.5. Since the second derivative of the function is -2 < 0, you know that V gets maximized when p = 0.5.
Thought that was a good explanation! I'm just now learning about this in a statistical physics course and it's nice to have a non-physics explanation of it. :)
.....but it was no better than ok. Just ok. And if it was any better than ok, I wouldnt admit it, because I am cool, and I have a moustache in my dp. You know what David, fuck you
The video is great though one little caveat: the mean (μ or x̄ ) is not the same as an expected value (E[X]). Statements like this make things just more difficult and confusing. The (arithmetic) mean is the sum of of all values of set X = { x1, x2, ... xn) divided by the total number of values in the set. It refers to any existing in reality (known or unknown to us) set or lists of values, like samples, populations and so on. Expected value (E[X]) refers to an event in the future and is the most likely probability of what we can expect to get as a value in the said future event. Yes, if you are considering drawing a sample with a large enough n, what you can expect more or less is that E[X] = μ (the mean of the population) given that you are looking at discreet or continuous distributions, but E[X] = p (proportion of the population) if you are looking at binary Bernoulli distribution.
what an explanation with Moment of Inertia and traffic! you are such a good explainer but why are you expressionless! don't take it seriously! good job!
Wow. To calculate the moment of inertia about a parallels axis is actually the 2nd moment subtract the 1st moment squared??? The moment all moments come together.
why p(x) = 1 in the continuous x example?? Because the area under the curve has to be 1? So if the augment of p(x) expand to [0,2], should p(x)=1/2?? ...Thanks for any replies in advance.
While I liked the lecture, it did not answer the airport question at all. By the mathematics shown then average and variation of times are same for both the trips. So, the difference is only psychological?
Very informative video series! My main comment would be to suggest that professors refrain from reading verbatim. It makes the content delivery dry and monotonous.
They describe other features of the distribution. For example the third moment is skew. If the data is skewed, the mean will no longer be at the highest point of the distribution. It also tells you that the mode (number that occurs most often) will be shifted. In a real world application, stationarity is a measure of stability in data. If your moments remain relatively unchanged over time, the data is stationary. Stationarity is a requirement in time series models such as those use for financial data.
"Throwing away information is the only way to fit the complexity of the world into our brain. The art comes in keeping the most important information." 2:16
i really respect my professor, but man the guy in video is 100 times better in every aspect.....
100%
@@benmackenzie NOPE, figuratively 10000%... if his respect as real is 100%...
"Throwing away information is the only way to fit the complexity of the world into our brains " - Sanjoy Mahajan
That moment (ha!) when you've been blundering through 5 years of statistics classes and you finally understand what a moment actually is. This was a super clear video and I liked the airport example.
btw the "(something I can't understand)" in the subtitles at 9:04 is "rises to a peak in the middle".
He is simply saying that the variance of the distribution is largest when p = 0.5. Since the variance of the distribution , V, equals p(1-p) = p - p^2, take the first derivative of this function: dV/dp = 1-2p. Setting it equal to zero gives its optimum: p = 0.5. Since the second derivative of the function is -2 < 0, you know that V gets maximized when p = 0.5.
I found Sanjoy very easy to follow, simple but effective examples provided, thank you!
This guy is awesome. Explains things clearly.
Thought that was a good explanation! I'm just now learning about this in a statistical physics course and it's nice to have a non-physics explanation of it. :)
I really love how he casually makes reference to other discipline
Appreciate the moments fam.
Thanks for the lecture. It was very helpful for studying for my engineering probability exam.
I found this okay - interesting topic, and a lecturer who knew the topic well enough to teach it in a logical and informative way.
.....but it was no better than ok. Just ok. And if it was any better than ok, I wouldnt admit it, because I am cool, and I have a moustache in my dp. You know what David, fuck you
That's an AI programmed professor. The eyecontact and the way he is speaking. Cool.
But his lecture was very cool
The video is great though one little caveat: the mean (μ or x̄ ) is not the same as an expected value (E[X]). Statements like this make things just more difficult and confusing.
The (arithmetic) mean is the sum of of all values of set X = { x1, x2, ... xn) divided by the total number of values in the set. It refers to any existing in reality (known or unknown to us) set or lists of values, like samples, populations and so on.
Expected value (E[X]) refers to an event in the future and is the most likely probability of what we can expect to get as a value in the said future event.
Yes, if you are considering drawing a sample with a large enough n, what you can expect more or less is that E[X] = μ (the mean of the population) given that you are looking at discreet or continuous distributions, but E[X] = p (proportion of the population) if you are looking at binary Bernoulli distribution.
super cool, super awesome!
thanks for the lecture MIT!!!
I want to be teached by this kind of teacher,Respect.
This is really well explained. Really insightful.
what an explanation with Moment of Inertia and traffic! you are such a good explainer but why are you expressionless! don't take it seriously! good job!
I hope someday MIT OCW uploads a video on Moments and Centre of mass in Calculus not the one in Rotational Dynamics
Thank you -
this was very helpful
🥰
This was really cool and really helpful. Thanks.
thank you for the clear explanation!
Such an interesting explaination! Love it
Loved the explanation!
Wow. To calculate the moment of inertia about a parallels axis is actually the 2nd moment subtract the 1st moment squared??? The moment all moments come together.
Beautiful right, I wish I could get that though, I will be coming back to it.
what a great teacher
Very nicely put, thanks!
Superb!
This is so good.
It is amazing video
Great video, thank you!
15 min video all important aspects covered
nice video!
why p(x) = 1 in the continuous x example?? Because the area under the curve has to be 1? So if the augment of p(x) expand to [0,2], should p(x)=1/2?? ...Thanks for any replies in advance.
yes, I think your guess was right. refer to: en.wikipedia.org/wiki/Uniform_distribution_(continuous)
not often, no such thing as fullx or comx or dependx, can say any nmw is ok
nice.
looks young for his age
While I liked the lecture, it did not answer the airport question at all.
By the mathematics shown then average and variation of times are same for both the trips.
So, the difference is only psychological?
Very informative video series! My main comment would be to suggest that professors refrain from reading verbatim. It makes the content delivery dry and monotonous.
1000th like!
What what do higher moments mean? what can you do with them?
They describe other features of the distribution. For example the third moment is skew. If the data is skewed, the mean will no longer be at the highest point of the distribution. It also tells you that the mode (number that occurs most often) will be shifted.
In a real world application, stationarity is a measure of stability in data. If your moments remain relatively unchanged over time, the data is stationary. Stationarity is a requirement in time series models such as those use for financial data.
@@DimitriBianco thanks for info
SUTD gang assemble
LOTTERY ?!!!
u guys are racist. look at the value and not the person
This professor put me to sleep