Maximum Likelihood For the Normal Distribution, step-by-step!!!

[@statquest]

Correction: 2:39 I said likelihood=0.03 for mu=30, but mu=28 is in the equation. Support StatQuest by buying my books The StatQuest Illustrated Guide to Machine Learning, The StatQuest Illustrated Guide to Neural Networks and AI, or a Study Guide or Merch!!! statquest.org/statquest-store/

[@Leo-sh1ih]

I think another error at 2:13 : shouldn't it say "likelihood of the curve given these data" rather than "likelihood of the data given this curve"?

[@hengdao1507]

Thank so much 🙏🏻🙏🏻

[@jungjunkim9824]

error bammmmm

[@fahadfardan]

I think the 32 is not right at 13:47. How it was 32 then became x ?

[@statquest]

@@fahadfardan x_1 was defined as 32 at 5:52.

[@sergior.m.5694]

This channel, along with 3blue1Brown make me feel like a mathematician who is actually discovering this techniques for the first time in a logical way, rather than just handed to me through some obscure formulas that one just take for granted, because most academics forget about the importance of visual intuition.

[@statquest]

I'm glad the video is helpful. :)

[@ianstats97]

statistically, academics cannot teach 99% of the time. Certainly a very skewed distribution

[@ian-haggerty]

Amen.@@ianstats97

[@freshprinceofPersia]

I'm a teaching assistant in stats at both UCL and Birkbeck (University of London), and I can say, hands down, I have rarely ever seen teaching as phenomenal as this in stats and maths. I wish I had access to your videos when I was learning, and struggled with all these topics (with teachers who didn't have anywhere near as as much commanding knowledge, and tended to over-complicate things), and not only, now, learn from you how to teach effectively (and obviously, still, a lot of maths & stats :). You don't begin to appreciate how much in-depth understanding a teacher has, to make stats&maths so seemingly simple and quick to swallow, until you start teaching these things yourself. Bravo! (This is one of my few comments on anything online ever)

[@statquest]

Thank you so much!!! :)

[@vikranttyagiRN]

Thank You for acknowledging Josh's absolute awesomeness

[@haleemamisal2432]

lol im a phd candidate at imperial and have no one teaching me :( . What is it with Russel Group

[@freshprinceofPersia]

​@@haleemamisal2432 Unless you end up in a good group with either a supervisor who is still active in getting their hands dirty with experiments and etc., or strong postdoc(s) in your group (edit: who are obliged/willing to help), PhD studentships can be like walking in a pitch-dark forest with your hands tied behind your back whilst having overdosed on hay-fever medication. It's ridiculous! I would take a strong and/or enthusiastic group/leader in a shitty uni over a shitty group/supervisor at a Russel-group/famous-department/uni any day.

[@sudiptabasu96]

@@statquest Great videos. Thanks a lot. What you really do to create these animations and graphs.

[@denisepatrick5547]

Some heroes do not wear capes......You are the real MVP!

[@statquest]

Thank you! :)

[@shalompatole5710]

Absolutely man. AMAZING VIDEO. There is so much effort and you have done a great job explaining a concept I was struggling to understand.

[@wennie2939]

Totally agreed. Josh is the BEST EVER!

[@shalompatole5710]

Give this man some Nobel Prize already. Peace, Economics even Literature will do. This sort of genius shouldn't go unrewarded.

[@statquest]

Thanks! :)

[@deepanshhh]

And if you can, please support by donating!

[@liezeltamon6354]

Dont forget music! 😂

[@menensa]

@@deepanshhh Amen

[@jabroomunda]

True for assisting nobel with BAM BAM .. BAM !

[@dahailiu2067]

OMG again this is the best MLE explain I've seen ever in my life.

[@statquest]

Thank you! :)

[@aremuoluwakemisola4187]

Thank you so much for this beautiful video. Thank you for making it exciting for me. I was just reading through my class note and i realized my lecturer left a lot of holes for me to fill. Your video has helped me tremendously. I am so grateful for this ❤❤

[@statquest]

bam!

[@akjdl5734asdf]

Joshua you are a hero! Truly a man of the people. Bless you kind sir

[@statquest]

Hooray!!! Thank you! :)

[@ritardstrength5169]

Thank you sir. I just suffered through a Math Stats class at a well-regarded graduate program that never explained MLEs as well as this short video.

[@statquest]

Thank you!

[@vipulvivek3874]

I was reluctant to start this video, seeing its length. I thought it will be some other university guy explaining it mundanely. I am glad I clicked. Even more glad that I was wrong.

[@statquest]

BAM!!! :)

[@olivierphilippe8686]

I am amazed how you teach these concepts and make them easy to understand. It is the first time I fully understand the standard deviation. Having this 'Eureka' moment was only possible because of your effort and your skills! You are really good! Thank you so much!

[@CatherinePryde]

Truth is even after years of working extensively with data, it is not only always informative to go back studying the most basic concepts possible in Statistics but also a real relaxing moments to listen to you teaching. It takes my head off overcomplicated matters, cleanses my reasoning and lets me walk out of this 20-minutes coffee break feeling more refreshed than any caffeine intake. Thank you !

[@statquest]

Hooray!!! Thank you very much! :)

[@chyldstudios]

One of the best descriptions of Maximum Likelihood ... in the UNIVERSE

[@parambole8671]

I spent 8 grand to learn ML in college and yet didn't truly understand what MLE is. Learned it for FREE on StatQuest. You Rock

[@statquest]

Thanks! :)

[@MohamedKhaled-el7vv]

If professors in universities explain like that the world will be a better place.......really thank you so much you are awesome

[@statquest]

Wow, thank you!

[@bin4ry_d3struct0r]

Watching a step-by-step differentiation of the Gaussian PDF has been on my to-do list for a long time. Thank you so much for this!

[@statquest]

Thanks!

[@lizzzylavender]

Ahhhhhhh I’m so mad! I found this channel while studying for my stats FINAL and it’s so good. My life would have been so much easier this semester if I had found this earlier! You explain things so intuitively so I always understand what is really happening instead of just watching numbers move around completely confused. You’re doing a great thing man, wish I could have been able to use your channel more haha.

[@statquest]

Thanks so much and good luck! :)

[@lhansa462]

I am truly staggered of how well-made this explanation video is. A lot of textbooks don't bother to explain their derivations and proofs, as they consider them to be "self-explanatory". Thank you a lot Mr. StatQuest, I learned more through your videos than in any statistics lecture! Keep up the good work!

[@bobbywu7701]

This explained what I tried to learn in our uni course for 3 weeks in just 20 minutes. If the teacher just showed the class this video there wouldn't be any confusion anymore

[@statquest]

bam!

[@sakhawat3003]

You know, how do I feel right now after taking this lesson? I feel like I had a very bad stomach after lunch and just gotten out of the toilet. It feels so calming and relaxing.

[@statquest]

dang

[@carylannebeltran]

You are a true hero!! Especially now with online classes and everything. Thanks soo much! This lesson was super intimidating to me, but learning from this video has made me realize it's not that hard at all. Good teaching makes miles of difference. Thank you so much!!

[@statquest]

Wow, thank you!

[@FootballRecaped]

I should have paid £12750 for this video rather than for my university! I have been reading slides and watching the lecture recordings from my university for over a week, but I couldn't understand. I understood everything clearly in this 20-minute video in one go. RESPECT!!!

[@statquest]

Thank you!

[@juansebastianpaboncubillos1024]

What a good video. I took me 7 year to understand it properly. U kicked out of the park.

[@statquest]

Awesome! Thanks! :)

[@UltraXan]

Jesus H-Bar, I wish I had math this clear and well explained when I was taking my stats class. So many profs just skipping lines and jumping ahead in their proofs, expecting us to fill in the blanks. Now here I am in a robotics course looking at maximum likelihood estimation and this video is giving me the lesson I wish I had years ago. A+, kudos, cookies, high fives... you take it all!

[@statquest]

Thank you very much! :)

[@nightravens1953]

I'm a current graduate student in a Machine Learning class, and I just wanted to take the time to say thank you from the bottom of my heart! It's online (due to the pandemic) and my professor's videos are honestly hit or miss (and his MLE video for me was definitely a miss....) The example REALLY helped me wrap my head around what we are doing. Thank you so so so so much... definitely donating (or buying some merch lol) as soon as I'm able!

[@statquest]

Thank you very much! I'm glad my videos are helpful. :)

[@beniaminradomir9798]

Holy this videos must take lots of effort, but it is so worth it. If conveying a subject in a clear manner is the main goal, this dude is a 10/10

[@statquest]

Thank you! :)

[@Noobsaucer]

Man, I really really hope from the bottom of my heart that you teach actual classes somewhere IRL too. You could have been the the difference between me failing out of university because of math and stat and finishing it with flying colors. Too bad I only found you now.

[@statquest]

Thanks!

[@mhalls]

I wish my university classes were as clear as your explanations. Thank you!

[@statquest]

Glad you like them!

[@jonibeki53]

Man, you just explained my whole lecture topic clearly and fast. Thank you!

[@statquest]

Wow! That's awesome! Thank you! :)

[@HieuNguyen-so3et]

Hands down thank you! This video with its visual explanation probably just saves me from enormous self-doubt and dropping out of my degree. I wish profs would put in the time to give you such illustration to help you understand, rather than pages of words and functions that confuse you even further.

[@statquest]

Thanks!

[@WhatTheGuiz]

wtf man how are you not president yet

[@johnjenkins4636]

I thought the U.S always choose the craziest to be president.

[@MyGaurav12]

This is the most intutive yet thorough explaination of MLE I have ever seen. Thank You so much Dr. Starmer.

[@statquest]

Thank you very much! :)

[@eriboyer2229]

Thank you Josh for this amazing StatQuest. It is people like you who keep learning to be very fascinating.

[@statquest]

I appreciate that!

[@carl6167]

What a hero. It takes a lot of time to do things in such detail that even the worst could still understand everything without having to ponder at why a step is valid ! GG

[@statquest]

Thank you! :)

[@bill_nj8543]

These videos on MLE are really wonderfully thought out and presented - very helpful in getting an intuitive handle on this important topic.

[@statquest]

Thank you! :)

[@MrOlisiko]

I rarely leave comments, but this was just so greatly explained that I had to express my appreciation for the video creator. Well done!

[@statquest]

Thank you!

[@อนรรฆวรรณภาสชัยยง]

This Channel keeps getting better and better.

[@statquest]

Thank you! :)

[@josy4767]

I really felt like you were telling me a bedtime story here, and rewinding was like asking you to go over the good bits. The ending of and the mean, equals the mean, and the standard deviation equals the standard deviation, was a pretty good ending.

[@statquest]

Hooray! :)

[@Learner_123]

Classic. I have seldom seen a teacher taking his students/audience from the base of the hill to the top in such a smooth fashion! Excellent. P.S. I can only pity on those who disliked this video, better get admitted into kindergarten :)

[@statquest]

I love this comment!!! Thank you. I love the analogy - some teachers just yell down from the top of the hill, other teachers have heard what the top of the hill is like, but have never been there themselves, so they just repeat what they have heard, and other teachers, like sherpas, know the way and are willing to do the trek. Also, I think of the "likes" and "dislikes" as a lesson about the world. The "dislikes" tell me that no matter how I try, I can't help everyone. However, the "likes" tell me that if I try really hard, I can help a lot of people - and that's what motivates me.

[@Learner_123]

@@statquest Keep up the good work ✌️. Would you please also consider posting a similar video on cramer rao lower bound (CRLB)?

[@MohammedBakheet]

You just explained what my teacher couldn't in three lectures, I wholeheartedly thank you, keep it up

[@statquest]

Thank you! :)

[@marc-antoinediot4315]

That is absolutely amazing : I'm from France so English isn't my native language, though I still understand it better than with my french teacher lessons! Hundred thanks

[@statquest]

Wow, thank you!

[@stallman3738]

After reading several pages and books, this is the first time I really understand that this is. Thanks alot

[@statquest]

BAM! :)

[@ashumohanty566]

you give me clarity about likelihood function thank u sir

[@donnymac575]

This is the best/clearest explanation of MLE I have ever heard.

[@statquest]

Thank you!

[@777bloomingdale]

Dear StatQuest, Great explanation. Please do video on MCMC metro polis Hastings and Gibbs sampling.

[@carlosdanielgt]

Hardly comment on KZbin videos but this one really deserves a big thank you. This material is pure gold! You made me understand concept's as never before.

[@statquest]

Thank you! :)

[@solaweng]

Every time when I have a new stats related course, I always use statQuest for a quick review. Cannot recommend more!

[@statquest]

Awesome!!! :)

[@maxipaxi1892]

What an incredible way to show how the formulas for the mean and standard deviation of a normal distribution are found! Videos like these make me enamored by statistics all over again

[@statquest]

Thanks!

[@kiveynen]

10 / 10 presentation skills :D. Love it.

[@statquest]

Thank you! :)

[@coldnlonely]

Your ability to explain this so well gives me goosebumps.

[@statquest]

Ha! Thank you. :)

[@thongnguyen1292]

Triple likes!!! Can't wait to see videos on more advanced concepts

[@statquest]

Thank you!

[@yatta4059]

I involuntarily watched this video with my mouth wide open because I couldn't believe that within 5 minutes into the video I understood what three 3 lectures+script couldn't explain ;) Keep up the good work, Josh

[@statquest]

Thank you! :)

[@jiji89960]

the *CHAIN RULE* dramatic atmosphere intensifies

[@statquest]

BAM! :)

[@Cld136]

I have never understand MLE this clear until now in my life. Thanks for excellent video. Subscribed and Liked!

[@statquest]

Awesome, thank you!

[@sumantabanerjee9728]

at 2:42 you said likelihood=0.03 for miu=30 but miu=28 which was used in the equation.

[@statquest]

Yep, that's a typo.

[@thai19995]

Struggling with the Pattern Recognition course for a while. You, sir, are the true hero!

[@statquest]

Thank you! :)

[@XploreWithShishir]

how can one make things so easy....you are great.

[@statquest]

Thank you!

[@leosutcliffe8547]

I'm 2nd year Engineer stumbling through this stuff all semester, the lectures my professors have recorded just make me feel like a total idiot and really fuel the imposter syndrome... So thankyou so much for explaining so well! It's not only teaching me the stuff but it's given me a bit of confidence back!

[@statquest]

Thanks! I'm glad the videos are helpful.

[@abhisheksrivastava9970]

The absolute pleasure of watching this video can only be attained by sticking to the playback speed of 1.0

[@francescogiacomelli403]

Modern day true compliment in education

[@malharjajoo7393]

2x is the way to go kid

[@JMarwah]

@@malharjajoo7393 But then you spend less time enjoying a StatQuest video, and that's no fun. You can't 2x something this beautiful.

[@ritik9799]

Words can't describe how awesome this video is !!!! I literally stood up and clapped at the end of this video. Request all that benefit professionally from StatQuest's videos to kindly support the channel via means listed in the description. God I love this channel !!!!

[@statquest]

Thank you so much 😀!

[@undine8750]

I can't believe we just did all that and ended with like "2 = 2."

[@statquest]

I know! It's a little bit of a bummer. But now you know why we can use the mean and standard deviation.

[@undine8750]

@@statquest nahh not a bummer is just kinda funny

[@undine8750]

I did well on my data science test yesterday thanks to this

[@statquest]

@@undine8750 Congratulations! TRIPLE BAM! :)

[@yashchudamanpatil7477]

man u earned my respect i almost got cleared all my doubts in this covid semester since cant ask doubts to prof lively

[@statquest]

Thanks!

[@PavanKumar-ef1yy]

Excellent teaching

[@statquest]

Thank you!!! :)

[@James08091980]

Probably the best explanation of the Maximum Likelihood estimator I've ever seen. Well done.

[@statquest]

Thanks! :)

[@raminaassaoui6083]

You should sit on the Throne of maths.... I BEND THE KNEE :')

[@statquest]

:)

[@josefsieber8377]

I had been wishing for a broken down video of the process of logging the likelihood function for a while and I just found this. Thank you! This is awesome and one of the most helpful things ive seen all year

[@statquest]

Wow! Thank you! :)

[@fabianzh5577]

Bruh you're hilarious. You must be popular in Stats Land!

[@riddle-me-ruben]

By far the Greatest explanation on KZbin. No debates.

[@statquest]

Thank you very much!

[@sonicking12]

Can you talk about the EM algorithm? Thanks.

[@statquest]

Yes!!! I'll try to get to it as soon as I can.

[@goldenhawk1925]

This is one of the most beautiful videos I have ever seen on youtube. Thank you for what you do

[@statquest]

Thank you!

[@Ahmed000Saber]

You are the best.

[@statquest]

Thank you! :)

[@Mgggggggggggggggggggggg]

Thank you so much for all the hard work you put into the video. Believe it or not! I first watched your video when I was in undergrad. Now I moved to US to do my master’s I’m still here!

[@statquest]

bam!

[@aryandeshpande1241]

Double bam!

[@riddhimanna3450]

everytime you went BAM!! I couldn't help laughing!!

[@statquest]

:)

[@fizoolplayer]

I just can't thank you enough. After college I'll definitely donate to your channel, with my first salary ! I don't understand why my college prof can't explain it simply like this.

[@statquest]

Thank you very much! I'm glad my videos are helpful! :)

[@hangyutian]

"I double checked" Hahaha

[@statquest]

:)

[@minyoonara]

this was AMAZING! i am currently taking machine learning course, and the teacher gave us these formulas to memorize without any derivations. i was looking for something exactly like this :) thank you!

[@statquest]

Glad it was helpful!

[@BilalAhmed-ib3yw]

triple BAM!!!

[@statquest]

Hooray! :)

[@xiajing6009]

Don't believe there are thumbs DOWN for this video!!! Super fan for this series!!! HERO!!!

[@farzanehaskari9703]

"chain rule" has a different meaning than what it is used for in this video.

[@raa__va4814]

this is by far the cleanest explanation on this topic EVER

[@statquest]

Thanks! :)

[@serkanmacit377]

university students see this kind of topics as a rocket science and lose their attentions to the ML. That is very nice and inspiring explanation, thank you.

[@statquest]

Thanks!

[@ezequielzion]

you seriously have no clue how much this video helped me bro, plus i love how you put in some humor so it doesn't become boring. you're amazing man :)

[@statquest]

Thank you very much! I'm glad the video was helpful. :)

[@김성준-i5p9f]

This explanation is beyond phenomenal!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[@statquest]

Thank you!

[@mahdimantash313]

The whole vedio I was just waiting for that TRIPPLE BAM ... man what a genius way to present knowledge

[@statquest]

Thanks!

[@silviapetrova8562]

holy god. one of the few times i had cry from the beauty of math. thank you

[@statquest]

Thank you!!! :)

[@kallihale5197]

This made so much more sense than everything else I've seen on the subject. Thank you so much.

[@statquest]

Thank you!

[@abdoulayely8284]

I wish I could like your videos a million times. I barely comment on youtube but I wanted to thank you josh for such incredible resources you are providing to us. You are saving lives out there :)

[@statquest]

Thank you! :)

[@indie209]

You're the hero Gotham deserves, but not the one it needs right now

[@niccolobaronio7555]

Thank you so much for this video! I'm preparing my Statistic Exam and this is gold Greetings from Italy

[@statquest]

Good luck! :)

[@because2022]

I can clearly see your dedicated efforts to create such amazing content which is explained in depth. Hats off to your commitment. Thank you so much.😀

[@statquest]

Thank you!

[@anuraggarg1209]

Thanks for saving me man! I will promote your channel as much as I can in my university

[@statquest]

Thank you very much! :)

[@MisbahAnwaar1988]

I was struggling with a research paper n using restricted maximum likelihood estimation for analysis... n this video made me understand the whole thing clearly!!! Bam * infinity!!!

[@statquest]

Hooray! I'm glad the video was helpful. :)

[@rajkmr15]

wow. Never seen someone explaning maximum likelihood to look this ease. Hats off :)

[@statquest]

Thanks a lot 😊

[@xuyangli4324]

Watched the whole video at X2 play speed. Saves me so much time understanding what is ML

[@Saint.Laurent.Jacket]

This video just made me pass my Statistical Inference unit....Thank you so much!!!!

[@statquest]

TRIPLE BAM!!! Congratulations!!!!! :)

[@mr.luvnagpal7407]

seriously amazing you are the best teacher in the world no words to explain how much helpful it was thank you so much!

[@statquest]

Thank you! :)

[@akshaymathpal9111]

You are making statistic fun, enjoyable and most importantly easy to understand.....wait for it.....(infinite)*"bam!!!", Thanks for clearing our doubts.

[@statquest]

Thank you! :)

[@dsagman]

That was amazing. I did not see the surprise twist ending if mean and standard deviation coming till you got there. I was a math major and always avoided stats because my classmates said the theorem proofs were so hard. Your videos illuminate those dark corners.

[@statquest]

Thank you very much! :)

[@vinhnguyenthi8656]

overjoyed, when I was watching your other videos of logistic regression, but I don't understand the pattern in the saturation model. I went back to looking for your videos to see more. I saw this video, thought this might be the knowledge I needed. When I finished watching, it did not match the answer I was looking for at first, but it was an unexpected answer for me. oh, all of a sudden you helped me understand the curve Why normal distribution like that is built mathematically, great, thanks for your channel for helping me Understand the difficult knowledge that I always wonder about when studying statistics. Thank you so much, I learned a lot from your channel

[@statquest]

Thanks!

[@BLooDy21HD]

Watching videos like that make me wonder why my math teachers were so bad at explaining even the most basic stuff like (a+b)^2 and went on by saying: it works because i say so. Not surprised so many people suck at math and most of them have to rely on online videos to explain stuff. Thank you!

[@statquest]

I'm happy this helped!