4. Stochastic Thinking

MIT 6.0002 Introduction to Computational Thinking and Data Science, Fall 2016
View the complete course: ocw.mit.edu/6-0...
Instructor: John Guttag
Prof. Guttag introduces stochastic processes and basic probability theory.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

[@user-or7ji5hv8y]

you can tell he's a great teacher because he's able to illustrate key points with simplicity and lays out the major paradigms ahead, like predicting the road ahead before we get there.

[@daxtonkeaton1180]

i know Im randomly asking but does anyone know of a method to get back into an instagram account?? I was dumb lost the account password. I would love any tips you can offer me

[@carmelobruce4821]

@Daxton Keaton instablaster ;)

[@daxtonkeaton1180]

@Carmelo Bruce thanks so much for your reply. I got to the site on google and Im waiting for the hacking stuff atm. Seems to take quite some time so I will get back to you later when my account password hopefully is recovered.

[@daxtonkeaton1180]

@Carmelo Bruce it did the trick and I now got access to my account again. I am so happy:D Thanks so much, you really help me out!

[@carmelobruce4821]

@Daxton Keaton Happy to help xD

[@FelipeNovaesRocha]

Man!! The pace him teach, the way explain your toughts process and the humor its like we are there just talking informal conversations, taking some afternoon coffe, relaxing. Its just amazing! I can note he its there in the present without rush, without anxiety, enjoying the exploration with you. John Guttag, thank very much!!

[@edwardblack9263]

MIT OCW and all these professors, thank you truly for sharing all of this

[@alanmainwaring1830]

This Guy is about my age and I can see he has much Wisdom in his teaching style, the pace is just right and using coding simulation builds up your intuition of getting a real deep understanding of this very difficult area. I have looked at many web links oh this topic of Stochastic processes all you usually get is boring formal definitions with ambiguous terminology, that is cloaking ignorance in terminology. This guy realizes it take really good examples to build up intuition and doing it slowly and carefully. What a great teacher

[@Random-sm5gi]

Thank you for providing high quality free content from MIT professors.

[@ericmcnally5128]

Thank you so much to everyone at MIT for making this kind of content available.

[@leixun]

*My takeaways:* 1. Uncertainty in the world 2:40 2. Simulation models 46:40

[@carolinanateldemoura1168]

Thanks, MIT. Excellent!

[@guruwebltd7746]

What an excellent teacher of knowledge

[@shobhamourya8396]

Enjoyed the explanation of 'seed' for pseudo-random numbers.

[@----5497]

4:43, Professor: "When we all know quantum mechanics", Me:"??????????????"

[@SalayTV]

Awesome teachers !! (y) thank you mit

[@lucashoww]

Thank you MIT!

[@20060802Lin]

Simulations are fortune tellers while optimizations are success books

[@mohitagarwala3281]

Well, Indians aren't always counter factual, but sometimes we do😂........ You are an amazing teacher 😊😊😊

[@europebasedvlogs1251]

Wdym

[@qazaqtatar]

Always well prepared professor

[@mohankumargajendran528]

Thank you! you gave the definition I was looking for.

[@huxiaoyang4548]

Thank you,MIT!!!

[@Jndstudioslike]

Thank you🎉

[@lee_badda]

Broncos joke is spot on sir!

[@17teacmrocks]

that's pretty awesome they rotate professors.

[@moart87]

Cool talk prof Guttag!

[@truptpatel2597]

it's program that describeeeessssss a computationnnnnnn that provideeeeeeessss an informationnnnnnn about possible behaviors of system.

[@donsurlylyte]

ran the sim a million times, in about a second. still blows my mind that computers are so fast

[@afuzzycreature8387]

i wish they were faster, I can still spool up useful things that will take a week

[@valor36az]

Excellent lecturer

[@mt.erebus3370]

Love the jokes, what a dry audience...

[@Marc-tm4xh]

The students aren't in the mix unless someone asks a question

[@hinkhall5291]

Sometimes I don’t laugh cause I’m not smart enough to understand the humor. I’m dumb. But funny enough I do remember the story of Oedipus Rex because my pops told it to me when I was a kid.

[@sadiqamore3958]

Because they are MIT

[@scottt7009]

Socially awkward kids, probably

[@akbarrauf2741]

thanks,mit

[@bengus2069]

6:12, "Um, professor I think you forgot one.. Namely, one head and one tail but the other way around."

[@javierblancosartori]

thanks fot this material!!

[@TheJustinmulli]

16:40 - Declaration of Independence *Nicholas cage enters the lecture hall*

[@jamesspacer7994]

I love this prof 👍🏻😂

[@alute5532]

2 coins it not causally non deterministic Predictive nondeterminism Use code for running simulations (if we have a general idea of the density function on hand) Only then simulation is possible Where simulation provides info about a (possible behavior) of a system of interest Possible behavior :ad in stochastic Descriptive : not prescriptive Only describe w possible outcome (not hoe to achieve it) Different from optimization models That is prescriptive Tells you how to achieve an effect Hey most value out of your problem (Or minimize your loss) Simulation (What if scenario answer) If you do this, here is what happens (not how make something happen) Only approximation to reality (not reality) Models can be erroneous as well) (biased to the writer /coder) All models are wrong but some are useful -george box When use simulation 1. Mathematically intractable 2. Extract intermediate results 3. Can play what if game scenarios how: refining it recursively Birthday : assume any distribution we assume (all on our assumption)

[@jack.1.]

What we learnt is that in reality simulations and approximation is superior to exact value mathematics. As an economist I agree.

[@rosh70]

Hate to agree with you, but I do. Also, coz' I'm a fan of 'exact value' mathematics. LOL

[@poppys34]

I had to look it up to see if he was right... Yes, the Broncos lost to the Pats 16-3 on December 18, 2016.

[@user-ej7ss8ei2g]

I think he was just joking and rooting for the Pats.

[@kashmira_zambad]

P(that nothing has a probability of 1)=1 , refer 4:30

[@StevenSmith68828]

I did a lot of this by just trial and error not knowing wtf I was doing to make a 21 counting game. The weird thing I found was that going first is why it’s unfair. Since the probability of losing is not a factor in the first round. ( Its Felony to use card counting devices fyi lol)

[@CultofThings]

What were the coins though?

[@許哲瑋-m7c]

Can someone please explain what the "N=100" means in the birthday problem? > Actual prob. for N=100...

[@Raviarun]

N=100 represents the number of people in a group. Can be called the sample size. If there are 100 people, what is probability that at least 2 or 3 people have same birth date is the simulation about.

[@charismaticaazim]

29:54 How do we know the number of samples required so that the estimated probability is equal to the actual probability ? Thanks.

[@whatsupbudbud]

13:01 Can someone explain why you divide probability of 1 by 6 to the power of 5 in order to get the probability of "11111" happening?

[@tahirhussain5618]

We can get 6 to the power 5 different combinations if we roll 6 dice. Only one of them is "111111". So the probability of getting "111111" is 1 out of 6 to the power 5 , hence 1 divided by 6 to the power 5.

[@aghileslounis1891]

1 is how many times do 11111 is available in the set (11111,11112,11113,...66666)? only once, so it's 1. 6 is the number of all possible events (in this case it's a series of integers 1 2 3 4 5 6, in another context it's either, "A' "B" ...). 5 is how many time do we repeat the process? in our case it's rolling a dice. One another way to get the result is, the probability to get 1 is around 16% if you roll the dice once, now the probability to get 11, is 16% now becomes the 100%, and it's then 16%, so it's 16x16 /100= 2.56%, repeat this 4 more times, you get 0.0128% if you divide this by 100 you get the probability in the range 0-1 which is 0.000128.

[@alanmainwaring1830]

@@aghileslounis1891 Be careful here don't confuse permutations with combinations. Think of lotto we do not think about the ORDER of the numbers, total number of permutations is 6 to the power of 5 number of combinations is 6 to the power of 5 divide by 5!

[@visunashokkumar1782]

Soo did the broncos lose??

[@محمدمصطفى-س9ع]

what was the third fact about the simulation I didn't get it?

[@kepstein8888]

Schrodinger's quarters.

[@hektor6766]

The fallibility of Logical Positivism demonstrated: Maybe your epistemological sample wasn't big enough. Credit to von Mises for the Birthday Problem, though.

[@quocvu9847]

34:27

[@pengyifei5600]

ah...am I missing something? because the material in this class is dramatically different from the last one = =

[@kuldeepmeena7615]

Sir Stochastic Models and Applications vs random processes subject which is the best elective .how to choose any one

[@anandiyer5361]

Can someone explain this piece of code in the extended birthday problem... possibleDates = 4*list(range(0, 57)) + [58]\ + 4*list(range(59, 366))\ + 4*list(range(180, 270)) aren't you creating duplicates in the list, when you multiply the same list 4 times? Is this a realistic situation?

[@Q_QQ_Q]

no

[@priyanksharma1124]

Schrodinger favored Quantum Physics unlike what prof said.

[@abduogalal53]

the guy with the camera have something wrong what the **** this like subtitles appears after the conversation

[@anonviewerciv]

I guess this course assumes its students have never taken a statistics class. 24:10 Pseudorandomness.

[@sarangan12]

February 12 ✋

[@apank21]

@4:20~ most of history people"" believed in newtonian physics?

[@adiflorense1477]

The world is really annoyingly hard to understand

[@srjshapthnktl4978]

nothing has the probability of 1.. so.. something is called nothing

[@kostikoistinen2148]

Copyrighted content on such a course is full of shit!

[@gianniskyriakou6577]

excellent teachers...cringy jokes though...like stop already

[@Robdahelpa]

what you consider cringy others dont, i rather have a fun learning environment, than a stuck up strict one.

[@jeffyboyreloaded]

are you kidding this guy is the actual perfect amount of funny

[@mt.erebus3370]

Yea, it's just you. I didn't find anything but your comment cringy.

[@CultofThings]

He'll be here all night