Such a respectful professor. His lecture still makes so much sense even in Spring 2022, after 11 years. That's why we study a whole sequence of random variable that works for an arbitrary amount of time.
agree, I am basically realizing if I take a course in my uni that is a element of the set of courses MIT has, I'm doing the MIT course to learn it. Every prof seems to be absolutely class.
He clearly states that probability and likelihood are synonyms in a colloquial sense, but likelihood has a very special meaning in the subject's context.
oh wow. This lecture is one of the best lectures on probabilities I've ever seen. It makes clear some of the reasons why I'm struggling with concept of probability until know. In high school, you're blindly taught these concepts and it never really made sense to me. This guy really does a good job of explaining probability models, from the idea of why you can combine two probability models to confusion caused by "distinguishability" ......
At 39:40 he warned about delving too deep in measure theory. He was right: I spent so much time with measure theory that in the end stochastic processes were just a footnote of the course.
Being much more on the applied side of mathematics, I agree. I've only spent a little bit of time in measure theory just to get the idea of the precise definitions and their relationship with probability theory. Now I'm taking a more applied approach to study stochastic processes since what I really need is to make probabilistic computations in real world models.
This awesome and respectful professor helped me to understand not only the subject but also why I have to study this. Thank you so much for your time and for sharing your knowledge with us. I've been struggling with this subject for a couple of weeks. Praise the Lord, I found you.
I'm glad he describes the philosophical territory before moving on to the math because for all my life my math teachers have failed to mention any of that.
As a Terence Mckenna fan this lecture is pushing all my fun buttons! I kept wondering if he was going to say to achieve true 50/50 odds, the coin would have to land on its edge every time!
I honestly run the video on x2 speed, and whenever I want to rehear something I can just go rewind in time it saves you a lot of time to go x2 speed, if it's too much x1.5 is okay
Events are the subset of the sample space, as explained here: *SAMPLE SPACE* ua-cam.com/video/leVm6xuKdlU/v-deo.html and *EVENT* ua-cam.com/video/leVm6xuKdlU/v-deo.html
i love this lecture but PLEASE fix the way it is recorded! can barely see the screen and it is very frustrating. Rather focus on the slides and stop moving the camera around. Thank you to the lecturer though for doing a wonderful job.
Sorry I think I missed that. I didn't watch the whole lecture. In 8:40 he mentions that "likelihood is a synonym for probability". I have however just realized that the word likelihood is used as a prescientific explicandum (and not as an explicatum).
I think there is a mistake in the proof of the last slide. I believe it should have lim(sum of Pr{B_m}) = lim(Pr{A_k})...excuse me for the rough equations.
Chris Oaks not every subset of the sample space is an event, only the measurable ones are. it is related to measure theory, and most of the time it's safe to ignore the measurability part for elementary courses. For more rigorous courses you will hear that all the time.
it would be great to have subtitles with these amazing lectures! is it that possible? it would be very useful for me because of my bad english. it is much easier with subtitles. just transcript (without synchronization) would be enough for me! thank you anyway!
The prerequisites listed in the syllabus, "Thorough understanding of elementary probability at the level of 6.041/6.341, which uses the following text: Bertsekas, Dimitri, and John Tsitsiklis. Introduction to Probability. 2nd ed. Athena Scientific, 2008. ISBN: 9781886529236. Some patience and affinity for careful mathematical reasoning." See the materials on MIT OpenCourseWare for more information at: ocw.mit.edu/6-262S11. Best wishes on your studies!
He is right though. He is also one of the leading experts in this entire field; and wrote some of the most renowned books in it, so he might be onto something.
Such a respectful professor. His lecture still makes so much sense even in Spring 2022, after 11 years. That's why we study a whole sequence of random variable that works for an arbitrary amount of time.
Brushing up my basics again here. No wonder why MIT is the best university in the world. Really love the lectures!
agree, I am basically realizing if I take a course in my uni that is a element of the set of courses MIT has, I'm doing the MIT course to learn it. Every prof seems to be absolutely class.
This lecture is amazing. I especially love the philosophy parts of this course.
Same here. I'm here for philosophy not engineering.
He is the inventor of LDPC codes and many more ideas. I did my research on his LDPC codes for my thesis. Awesome brain.......High Regards...
thank you so much for adding in subtitles! means a lot to people like me who have auditory processing issues but still want to learn :)
12 years and still fining it useful. May God bless you professor
He clearly states that probability and likelihood are synonyms in a colloquial sense, but likelihood has a very special meaning in the subject's context.
oh wow. This lecture is one of the best lectures on probabilities I've ever seen. It makes clear some of the reasons why I'm struggling with concept of probability until know. In high school, you're blindly taught these concepts and it never really made sense to me. This guy really does a good job of explaining probability models, from the idea of why you can combine two probability models to confusion caused by "distinguishability" ......
At 39:40 he warned about delving too deep in measure theory. He was right: I spent so much time with measure theory that in the end stochastic processes were just a footnote of the course.
Being much more on the applied side of mathematics, I agree. I've only spent a little bit of time in measure theory just to get the idea of the precise definitions and their relationship with probability theory. Now I'm taking a more applied approach to study stochastic processes since what I really need is to make probabilistic computations in real world models.
Any moment now, this guy's going to stop mid-speech and offer you a glass of sweet tea.
ha....seems like he's from the deep South somewhere... he must like Alabama football! Yea, Crimson Tide!!!
This lecture is more philosophical than mathematical. Love it!!!
You're not alone
I am thankful to OCW for offering these lectures. Its just quite unfortunate that the quality of video is not good enough to read the slides easily.
This awesome and respectful professor helped me to understand not only the subject but also why I have to study this. Thank you so much for your time and for sharing your knowledge with us. I've been struggling with this subject for a couple of weeks. Praise the Lord, I found you.
I'm glad he describes the philosophical territory before moving on to the math because for all my life my math teachers have failed to mention any of that.
Math teachers are not philosophically trained.
I'm falling in love with this professor by the minute! And I've only seen 12 minutes.
...too sexy!!!
As a Terence Mckenna fan this lecture is pushing all my fun buttons! I kept wondering if he was going to say to achieve true 50/50 odds, the coin would have to land on its edge every time!
He is truly a master. Randomness is compression of factors.
Good lecture. Im taking that class right now and i was feeling so confused, this Sir is clearing stuffs to me, thaks!
Very nice to hear wikipedia getting credbility for probability here. That is a good pointer
He's really good. Definitely at a much deep level and understanding.
I honestly run the video on x2 speed, and whenever I want to rehear something I can just go rewind in time
it saves you a lot of time to go x2 speed, if it's too much x1.5 is okay
Okay man but nobody cares
@@martinjanas3324 That was rude
This guy is really amazing! I really like this course and this prof!!!!
This is great. Brilliant lecturer, and I love his commentary
What is the difference between *SAMPLE* and *EVENT* ?
Events are the subset of the sample space, as explained here: *SAMPLE SPACE* ua-cam.com/video/leVm6xuKdlU/v-deo.html and *EVENT* ua-cam.com/video/leVm6xuKdlU/v-deo.html
The philosophical professor of engineering.
Such an amazing human being..!
Really like this professor. So great!
55:46 random variables’s expectation value
Congratulations professor Gallagher
stochastic process is study an infinite sequence of random variable.
Timeless treasure. Thank you.
I like this guy, he actually teaches
i love this lecture but PLEASE fix the way it is recorded! can barely see the screen and it is very frustrating. Rather focus on the slides and stop moving the camera around. Thank you to the lecturer though for doing a wonderful job.
+Lisa Chanderman This course has course notes that might be of some help. See the course on MIT OpenCourseWare for the materials: ocw.mit.edu/6-262S11
Dear +MIT OpenCourseWare, it is an amazing lecture, but unfortunately it's title is a misnomer.
:-(
infact this topic has been pulled in detail,good informative keep it up mit
thank you for speaking understandable English.
...howdy boyz!!!
thank you so much! a great lecture by a beautiful mind!
Sorry I think I missed that. I didn't watch the whole lecture. In 8:40 he mentions that "likelihood is a synonym for probability". I have however just realized that the word likelihood is used as a prescientific explicandum (and not as an explicatum).
This is such a great lecture.
I think there is a mistake in the proof of the last slide. I believe it should have lim(sum of Pr{B_m}) = lim(Pr{A_k})...excuse me for the rough equations.
...seems like a nice gentleman...can't help but like him!
What a groovy lecture. Lots of fun!
Lovely lecture. Thank you!
this is absolutely brilliant!
So, just what kind of "Awful things" happen when the union of events is not considered and event ( Around between 40:00 and 41:30)?
_Discrete Stochastic Processes, as you all know._
fuck.
great job men from algeria
does this course teach all the fundamentals required for learning stochastic processes
Very good lecture,sir
He looks awfully like Warren Buffet for some reason ...
+GlobalMacro Yes. I think so too. He reminds me of my grandma also.
+xiao Lin you mean grandPA right ?
He is....
@@xiao6322 What pronoun does your grandma prefer?
This is a great lesson. However the quality of the video is very low. Sometimes texts become unreadable.
The slides are available as a pdf on the course website
Truly intelligent.
Hi everyone, a question: what does he mean when he says, "I
Thanks. great lecturer.
"This function must satisfy the constraint that [w: X(w)
Chris Oaks not every subset of the sample space is an event, only the measurable ones are. it is related to measure theory, and most of the time it's safe to ignore the measurability part for elementary courses. For more rigorous courses you will hear that all the time.
it would be great to have subtitles with these amazing lectures! is it that possible? it would be very useful for me because of my bad english. it is much easier with subtitles. just transcript (without synchronization) would be enough for me! thank you anyway!
totally necessary philosophy part
Which is what he said.
great lecture .. hats off prof :)
Subtitles have many mistakes. Please have a look at it.
anyone know the prerequisite for this class since this is a graduate class ?
The prerequisites listed in the syllabus, "Thorough understanding of elementary probability at the level of 6.041/6.341, which uses the following text:
Bertsekas, Dimitri, and John Tsitsiklis. Introduction to Probability. 2nd ed. Athena Scientific, 2008. ISBN: 9781886529236.
Some patience and affinity for careful mathematical reasoning." See the materials on MIT OpenCourseWare for more information at: ocw.mit.edu/6-262S11. Best wishes on your studies!
@@mitocw thank you so much ! I love MIT class,It is always the best !
what book was he talking about when he said "Keller?" Is it the concepts i probabilty and stochastic modeling by sallie keller-mcnulty?
"Feller" , ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-262-discrete-stochastic-processes-spring-2011/course-notes/MIT6_262S11_back.pdf
www.google.com/search?q=killer+probability&ie=utf-8&oe=utf-8&client=firefox-b-ab#q=feller+probability
Wow... how cool... I didn't know they offered those. Very nice touch, even if they need improvement ;)
Why is it called stochastic calculus? It is stochastic process class right?
Discrete stochastic processes.
ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-262-discrete-stochastic-processes-spring-2011/
is the probability systems analysis course also provided by mit a sufficient prerequisite for this course?
great man!
The likelihood is not a synonym for probability. It does not have a density with respect to a Lebesgue measure!
Wow, this class is so dead. How unfortunate.
Make me wish I took my MIT offer, but my wallet says otherwise
I really doubt the probability that there is one single person gonna finish the whole series. No offence. Great video though
I'm going to watch through it once now to get an idea of what I'm working toward with calc and algebra. I'm sure I won't understand some of it :)
Anybody read the lecture notes , on page 3, the probability of rolling a die is assigned to 6^-n , n can't be a negative number ..
+nsharkasi x^-y = 1/x^y
w00t!
44:40 haha true
16:40
did he suggest Wikipedia? haha
He is right though. He is also one of the leading experts in this entire field; and wrote some of the most renowned books in it, so he might be onto something.