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

Calculating the maximum likelihood estimates for the normal distribution shows you why we use the mean and standard deviation define the shape of the curve.
NOTE: This is another follow up to the StatQuests on Probability vs Likelihood
Viewers asked for worked out examples, and this one is super mathy, but I just couldn't say "no"!

For a complete index of all the StatQuest videos, check out:

If you'd like to support StatQuest, please consider...

Buying The StatQuest Illustrated Guide to Machine Learning!!!

...or...

...a cool StatQuest t-shirt or sweatshirt:

...buying one or two of my songs (or go large and get a whole album!)

...or just donating to StatQuest!

Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter:

0:00 Awesome song and introduction
0:45 Overview of the normal distribution equation
1:41 Example with one data point
5:38 Example with two data points
7:35 Example in 'n' data points
8:08 Solving for the MLEs for mu and sigma
18:54 Review of concepts

Correction:
2:39 I said likelihood=0.03 for mu=30, but mu=28 is in the equation.

#statquest #MLE #statistics

[statquest]

Correction:
2:39 I said likelihood=0.03 for mu=30, but mu=28 is in the equation.

[sergior.m.]

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.

[denisepatrick]

Some heroes do not wear are the real MVP!

[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)

[shalompatole]

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

[akjdlasdf]

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

[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!!!

[olivierphilippe]

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 !

[dahailiu]

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

[vipulvivek]

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.

[HieuNguyen-soet]

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.

[binry_dstructr]

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!

[lhansa]

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!

[chyldstudios]

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

[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!

[nightravens]

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!

[beniaminradomir]

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

[lizzzylavender]

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.

[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!!