Expected Values, Main Ideas!!!

Expected values are part of the foundation of statistics and the reason why casinos don't go out of business all the time. Here, we walk through two examples that explain the concepts behind Expected Values and its fancy looking notation. BAM!
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0:00 Awesome song and introduction
5:09 Calculating an Expected Value
8:02 Expected Value notation
10:30 A more complicated example of Expected Values
#StatQuest #Statistics #ExpectedValue

[@statquest]

Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

[@adolfocarrillo248]

Thank you for sharing your knowledge. This one was clear as the Ganges river, I mean where the main stream rises, near the Himalaya Mountains.😉

[@statquest]

@@adolfocarrillo248 Thanks!

[@therealpattypooh]

Just purchased my copy of Guide to Machine Learning. The first time I saw a video of yours was just some days ago, it was about PCA, and I couldn't believe I understood its concepts. You're exceptional. Thank you, Josh, I'm just addicted to your videos; they keep me motivated!.

[@statquest]

@@therealpattypooh Wow! Thank you so much for your support! BAM! :)

[@efunchen]

Actually 100% of people in StatLand have heard of Troll 2 because you went around and asked everyone if they've heard of Troll 2 :)

[@statquest]

:)

[@satwiktutor]

bammmm@@statquest

[@Mr_ScrufMan]

@@satwiktutorquite possibly triple bammm

[@apah]

I binged your Statquest stat fundamentals and just finished it. Can't express how much it has helped me build a sense and create a solid base for my ongoing data science masters. The older i grow, the more i realize that in some areas of life, it is best to treat adults like the children they actually are in these specific areas. Unbelievably efficient. You're an amazing teacher who deeply understood how much repetition & maintaining a trail of thought is key (+ bite sized format). I managed to grasp an in depth understanding of most concepts with rarely if ever having to rewind thanks to the number of times you repeat and synthesize key notions. THANKS JOSH !!
(Also you're hilarious, and i genuinely love your music and overall vibe, i been going through rough times health & study wise and just can't believe how you made my week, and how you made me enjoy learning probas/stats again)
Cheers ♥

[@statquest]

Wow! Thank you very much! I'm really glad to hear that my videos are helping you. I also hope that your rough times will come to an end soon! :)

[@MADaniel717]

I like the concept of statland

[@statquest]

Hooray!!!

[@cwtrain]

Statistics at 10pm on a Sunday!? You better believe it! Woo!
_buckles up_

[@statquest]

Bam! :)

[@danspeed93]

Explaining clearly the expected values … I clearly understood them. Well done your mission is accomplished!

[@statquest]

Thank you!

[@mhdamayri2529]

I got very curious about Troll 2 and looked it up on the trivia part of the IMDB page it says :
"The entire cast went to a casting call hoping to be extras, and ended up in lead roles."
You can just imagine for yourself how the trailer looked like.

[@statquest]

bam! :)

[@nicolasabboud8577]

Your method of explaining concepts is unique. You made me love probability and statistics. Thank you a lot. 🌷

[@statquest]

Thanks! :)

[@ayomikunoyenuga821]

I already watched a video before this one to explain what Expected Value meant but when I came across Statquest, I knew I had to definitely watch this video
I wasn’t disappointed. Your real-life adaptions for statistical concepts are really engaging, Josh!
Kudos!

[@statquest]

Thank you! :)

[@chrisjm80]

Very clearly explained, thank you! Looking forward to the other videos in this series! StatSquatch FTW! 😄

[@statquest]

BAM! :)

[@ScottEdwards2000]

Great video. Can't wait to understand the n-1 thing. I've been waiting to understand that for a long time!

[@statquest]

Hopefully we'll get there soon! :)

[@physicsfaith]

You are going to be disappointed... Its a mathematical fact based on the degrees of freedom. What does that mean? If I told you 10 numbers added to 100, do you need to know all 10 numbers or with 9 do you know what the 10th must be because the sum told you to last bit of information? Its going to be just like that here.

[@ScottEdwards2000]

@@physicsfaith cool I'd love to hear more. It's interesting that only the standard deviation needs to be divided by n minus one not the mean

[@statquest]

@@physicsfaith It's related to that, but the actual derivation is pretty complex.

[@evanstoid]

@@statquest attempting to understand the concepts of degrees of freedom and the intuitive understanding of why we need a smaller denominator for estimating the sample variance has only deepened my understanding of my ignorance of those concepts.

[@arc7244]

I can't thank you enough! I owe you a lot... The world needs teachers like you 🙂

[@statquest]

Thank you! :)

[@alainleclerc4523]

isthere a better teacher than you on earth? i don't think so. you are absolutly amazing!! you master the art to make complicated things easy and pleasant. you are so wonderful!! thank you very much for all your efforts in those videos. each one is a gem!! be blessed!!

[@statquest]

Thank you so much 😀!

[@aysenurfidan1122]

As someone who started to learn to code, and then data analysis and now dying to learn about ML in her 45 without any relevant background, your videos are life saver! I can understand all and I am enjoying it! You make me want to learn more. Thanks a lot!!!

[@statquest]

Hooray!!! :)

[@blackmeteorite-rj3vw]

bro thank you for all that effort to simplify things

[@statquest]

Thanks!

[@jaquelinemoreira7385]

it's finally clear for me what the expected value means in practical. i'm amazed for it, Thank you so much!

[@statquest]

Hooray!!! BAM! :)

[@just_a_viewer5]

adore your videos so much, sir. thank you for helping me change my attitude towards this subject. may you get all the happiness you want

[@statquest]

Thank you very much! :)

[@AJK-a2j00k4]

The moment he says "it's time for Shameless self promotion" lololol!

[@statquest]

bam!

[@justingomez9615]

Bro, where was this channel all my life, cant believe I'm now stumbling upon this channel. Great Great style of teaching 👍

[@statquest]

Thank you!

[@kevinding1204]

This is super helpful thank you soooooooooo much. I tried to read the textbook definition and it was way too boring/complicated to understand (doesn't explain enough) while your video just makes everything much clearer for me. Thanks!

[@statquest]

Glad it helped!

[@kimiko495]

I wish professors in universities taught in this way. Thanks for making statistics so accessible. I felt very frustrated when I came here but now I am motivated to learn.

[@statquest]

BAM! :)

[@cananakca1408]

BAM!!! I am hooked on your videos! You make it so easy for anyone to understand.

[@statquest]

Hooray!

[@jasonfaustino8815]

THANK YOU! You really are a lifesaver. Wish all educators have your “teach it to a 5yo” approach. I really appreciate you showing the cryptic formulas and then explaining it to me like 5

[@statquest]

Thanks!

[@pptmtz]

Great job man, greetings from México City, you explain very clearly and the "translation" to fancy notation allows me to better understand some academic papers.

[@statquest]

Muchas gracias!

[@teosurch]

Thank you, so clear explanation and an example about the usefulness of the expected value with the calculation of a bet profit!👍

[@statquest]

Glad it was helpful!

[@mereraK]

I saw a genius here today; he explained complex concepts in simple way. Thanks!

[@statquest]

bam! Nice rhyme!

[@sxx2491]

dude you saved my life once again with your clear explanation and the proper example

[@statquest]

DOUBLE BAM! :)

[@yoshitareddy4137]

BAM!! You are the best!! Thanks a lot, your videos have been very helpful ❤️

[@statquest]

Glad you like them!

[@janilayturatkhankyzy1321]

Thank you Josh, the way you explain is a masterpiece!

[@statquest]

Thank you! :)

[@Veto2090]

StatSquatch knows there's a Troll 2 viewing party happening at the local theater and he's about to fleese us

[@statquest]

BAM!

[@apah]

BAAM it's finally here !
Wuan wuan .. can't wait for part 2 & 3 (initially came for the n-1 thing :p)

[@statquest]

:)

[@vinitbipinjain]

Thank you so much for an amazing video and the pdf!

[@statquest]

You are welcome!

[@adnanornab5134]

You explained beautifully. Thank you.

[@statquest]

Thanks!

[@numberexplorerchannel1827]

Million Baaamss. You just made all expected value confusions so cleeaarr. Salute👌

[@statquest]

Thank you! :)

[@LeCassiopeia]

I love you for creating this. This helps me so much.

[@statquest]

I'm so glad!

[@skysummer1586]

Exactly what I need right now!!! Thank you so much!

[@statquest]

Glad I could help!

[@raduandreicosmin]

Looking forward to part 2!
Continuous expected value is something I've been struggling to find a comprehensive, easy to understand explanation on.

[@statquest]

That should be coming out next week.

[@anashaat95]

Clear explanation. Thank you.

[@statquest]

Thank you!

[@faresmhaya]

I can't believe that I was never explained this concept in school. I memorized the name, I memorized the formula again and again every time I needed to use it, only to forget it afterwards, but I never understood the how and why. It's such a shame.

[@statquest]

I hope the video was helpful.

[@faresmhaya]

@@statquest It certainly was! Thank you for the work that you keep doing, and happy holidays!

[@farukapece]

Thank you very much for your very nice and clear explanation.

[@statquest]

bam! :)

[@kendesmarais9018]

Josh you are the best! Thanks so much for your helpful videos!

[@statquest]

Glad you like them!

[@tayyabhussaintahir]

You are the best, please keep making these wonderful videos.

[@statquest]

Thank you! Will do!

[@miguelcabrera9682]

Awesome video. Thanks!

[@statquest]

Glad you liked it!

[@bibekanandabhattacharjee952]

Fantastic, superb !!

[@statquest]

Many thanks!

[@anuragbisht1200]

Statsland growth of population is quite significant from "conditional prob." video to this one 😄

[@statquest]

bam! :)

[@rajns8643]

The explanation was as brilliant as expected :)

[@statquest]

Thanks!

[@vikat06]

Really good explanation!!

[@statquest]

Thank you! :)

[@koustubhmuktibodh4901]

Wow! what a great explanation.

[@statquest]

Thanks!

[@stephenmaharaj5230]

Useful and fun. Thanks.

[@statquest]

Thanks! :)

[@h-s7218]

Great and awesome video ever !

[@statquest]

Thank you!

[@abdullahshahid9051]

This is the best stats channel easily

[@statquest]

Thank you!

[@TrungTran-dp3ct]

hey Josh,
Thank you for all of your videos. Better than other online courses/resources, and it's totally FREE. You are GOD!

[@statquest]

Wow, thanks!

[@MarwinMachay]

Amazing video! Thanks for making stats clearer to us :)
Question: the expected value should be the same either sampling with or without replacement, right?

[@statquest]

I believe so. The idea is "what do we expect, on average".

[@mixalisk.5413]

Josh hello from Greece!!! Thank you for all of your videos. Could you please consider making 1 or 2 statquests about time series? No matter how much I searched i couldn't find something comprehensive

[@statquest]

I'll keep that in mind.

[@rashmik19]

Awesome content.....BAM!!! BAM!!! BAM!!!

[@statquest]

Thank you! :)

[@yorchais]

Best explanation ever!

[@statquest]

Hooray! :)

[@monilcharola6873]

Your videos are awesome !!!

[@statquest]

Glad you like them!

[@praveerparmar8157]

Super duper like for the video.
Pity on the Statsquach 😀

[@statquest]

Hooray! :)

[@gustavojuantorena]

Great video! Thanks!

[@statquest]

Thanks! :)

[@rishabhnarula1999]

great teaching, thank you sir. 👍😊

[@statquest]

Thanks!

[@emanelsheikh6344]

Thank you so much 🙏

[@statquest]

You're welcome! :)

[@Vanadium404]

12:15 Stats squach is the worst gambler ever 😂😂

[@statquest]

Totally!

[@Ra-pt6tx]

Great Job

[@statquest]

Thanks!

[@misnik1986]

excellent job

[@statquest]

Thank you very much!

[@catmeme4life220]

Troll 2 is going to be the all I can think of during the midterm ... thanks...

[@statquest]

:)

[@whiteroadism]

Thanks for the lottery system setup guide.

[@statquest]

:)

[@rishithashenal4048]

If you asked everyone if they had heard about the Troll 2 movie before, then the next time you are asking everyone has heard of it.

[@statquest]

:)

[@zahraeftekhar3308]

Great video! looking forward to other parts! Could you please also do a video on Dirichlet distribution and latent Dirichlet allocation. I am struggling with them these days :( that would be awesome!

[@statquest]

I'll keep that in mind.

[@playerdreamer181]

DUDE THIS IS SO COOL

[@statquest]

Thanks!

[@almonddonut1818]

Thank you!

[@statquest]

You're welcome!

[@bebarshossny5148]

lovely channel, subbed!

[@statquest]

Awesome, thank you!

[@ericdanielasi5983]

I sat through this and it's worth it.

[@statquest]

Thank you! :)

[@mysticalpotato2110]

Hi Josh, please make a video on degrees of freedom.. Thanks

[@statquest]

I would love to.

[@rashmik19]

Alone maths has never helped me to learn data science skills, it's a combination of maths, intuition and the physical significance of the concepts. I found all of them here on your channel.

[@statquest]

Hooray! I'm so glad my videos are helpful.

[@futbolscoop]

Thanks , keep it up sir

[@statquest]

Will do!

[@mohammedabrar2871]

A great video, keep help[ing out!

[@statquest]

Thanks, will do!

[@TheFobJang]

Loved it! And poor StatSquatch

[@statquest]

Thank you!

[@bablu_0k]

Dudeee... statsquach sure love to take risks 😂

[@statquest]

bam! :)

[@futureisnow5446]

Great man.🦁

[@statquest]

Thanks!

[@Andre_NS]

BAM! Very good 👍

[@statquest]

Thank you! 👍

[@ankitagrawalgeneral]

Dear Josh, Thank you for creating great videos and uploading in RUclips for us. I was watching your Logistic Regression video and I was struggling with cross terms between differernt features. Do you know any literature on how to include cross terms in the model?

[@statquest]

I believe you are asking about interactions. Interactions are when two features can influence each other. Like you might have two different drugs that help reduce blood pressure, and when taken separately, that's what they do, but when taken together, you might end up with something completely different (like higher blood pressure or something else). That's an interaction and the "x" term accounts for that. Unfortunately I don't know of any good literature on the subject.

[@ankitagrawalgeneral]

@@statquest Thanks for the answer. Yes you got it absolutely right. I will check it. Can you cover Louvain and Leiden clustering in your upcoming videos. I want to hear from you about these techniques which are frequently used in single-cell community. Thanks a lot.

[@rungrawin1994]

Love your explanation! Can you explain about LoTUS plsss.

[@statquest]

I'll keep that in mind.

[@ptxsv8705]

Omg this helps me understand so much quicker

[@statquest]

bam! :)

[@julieyananzhu1134]

Hi, Josh. Hope you can talk about mixed-effect model. And the pros and cons compare with GEE. Thanks!

[@statquest]

I'll keep that in mind.

[@tristanv6202]

I love these videos! They are perfect for understanding important fundamentals. One question tho... When making the bet you know you have 213 (N_total) people in StatLand. When you find the outcome of the first bet wouldn't you change the probability from the definite heard of (N_A) or not heard pile (N_B)? If so then shouldn't your expected value be different every time as you make the bet and is there a mathematical expression for what I just described?

[@statquest]

I'm not sure how the outcome of the first bet changes whether or not people know about Troll 2. Can you clarify?

[@bob_bobsen]

Loved the sly comment about textbook clarity at 08:10

[@statquest]

:)

[@ichimatsu8422]

"Make it look more cryptic" this man knows the struggle

[@statquest]

bam!

[@mbs8249]

Thank you

[@statquest]

You're welcome!

[@b3_66_varadlatkar7]

Your voice is like I'm hearing a podcast

[@statquest]

bam!

[@ChelseaaaL]

Love the content. But I guess that we might lose the bet because in the survey, everybody kind of heard of the troll 2 in being asked the question have you ever heard of Troll 2😂😂😂😂

[@statquest]

bam! :)

[@setarehbakhshi6047]

I loveeeeeeeeeeeeeeeeeeee your teaching method.

[@statquest]

Thank you very much! :)

[@pon-poncedie4963]

thank god I'm desperate to learn what school is trying to teach me. This was very good, as I was confuse how to read what the Big E was.

[@statquest]

bam!

[@vijayendrashrivastava9178]

Thanks very nice.. helpful

[@statquest]

Thanks!

[@momentum742]

best person to learn math from

[@statquest]

Thanks!

[@yitanglu6039]

Could you make an album collecting songs in your videos? Love those songs.

[@statquest]

Bam! :)

[@duy-nq]

Just have the interview a few days ago, guys!
They ask me the same type of question like the one in this video @@ and I'm fail to answer.
Now I understand why... lol

[@statquest]

Thanks for the tip! Hopefully you’ll do better next time.

[@govamurali2309]

Waiting for Stat quest on degrees of freedom❤

[@statquest]

One day it will happen! :)

[@sidkapoor9085]

Intuitive build-up and explanation.

[@statquest]

Thanks!

[@sharme_]

Super BAM!!!

[@statquest]

:)

[@christopherlauw1570]

i love your videos

[@statquest]

Thank you!