Expected Value and Variance of Discrete Random Variables

[@screwgoogleaccounts7111]

You took 8 minutes to do what my Professor has done in 17 pages of nonsense notes. I would be failing without this haha

[@vasofxakadze]

❤❤❤

[@Hind-t9j]

first video that actually explains the concepts instead of just applying the formulas, thank you so much

[@jbstatistics]

That's what I do here :) I'm glad to be of help!

[@jbstatistics]

Thanks for the compliment! I've got lots of good stuff on this channel, and I hope you find it helpful.

[@parthsarthy3611]

I wish my professor in university could teach students like jb does.Understood it in 5 mins.thank you

[@SilentRyd]

Most professors spend lecture on theoretical side of math and proofs of theorems. They only spend a minute or two on its applications and how to use it. JB focuses on that aspect which makes him great teacher for a lot of us including myself.

[@TG-wg4tw]

not only the prof but alot of book is confusing as he11 too. I'm currently reading the Information Theory book by Cover-Thomas and let me tell you, these E(x) just fly out from no where and a bunch of "information content" "surprise",... etc and basically means the same thing or completely different things but have the same denotation.

[@TG-wg4tw]

@@SilentRyd wtf learning those theorems and proofs for when you can't wrap your head around the idea ? It's like when you're nearly starve to death and some one comes in, instead of showing you how to hunt they teach you about the mammal evolution.

[@jcn268]

im learning this in college ,yall just learning this in uni?

[@mickeychan2007]

@@jcn268 I learnt this in 7th grade, just came here cuz it’s a great refresher

[@kokokiki]

I've watched so many videos on expected values and variance and this was the first one I was able to really truly understand. Thank you so much for being so thorough!

[@amylabelle6239]

All of these videos are saving my life, you are amazing at what you do JB.

[@jbstatistics]

Thanks Ami!

[@kaljamaha16]

I am so glad that I found this channel. I have been struggling with my university's probability and statistic course

[@roh_yinee5229]

My uni professor made this topic so confusing I got frustrated thinking I'm too dumb. But this vid explained it so well. Thank you Sir.

[@jbstatistics]

I'm glad to be of help!

[@黎銘-s9n]

It's my personal observation that professors are good at making simple facts complicated, which is precisely why parents pay the high tuition. They make an image of authority of something for themselves in front of learner by making easy problems difficult. People pay doctors generously when they are in severe pain, which is in the same blind spot of human nature.

[@thvbitch]

​@@黎銘-s9n exactly well said

[@ojussinghal2501]

The clarity with which you explain things, it's fantastic. Whenever I have a doubt, you clarify it in the very following sentence!

[@jbstatistics]

Thanks for the kind words!

[@ojussinghal2501]

@@jbstatistics You're welcome. I'm studying probability and statistics as a first-year student and your videos are helping out a great deal!

[@jbstatistics]

You are very welcome! I'm very glad you are finding my videos helpful. And thanks for the compliments!

[@Bitrey]

Sir thank you so much. No need for fancy university documents with so much theory and no examples, THIS is how you teach, so so clear.

[@jbstatistics]

Thanks for the kind words! I'm glad to be of help.

[@subconcioussplatter]

This is great. All the explanations are concise and I like that you clarify certain things so that you don't fall in to the typical traps. Thanks for the stats video, I can finally understand it :)

[@Pastozafaire]

Pure Brilliance! Well done! You are a GENUIS!!!

[@jbstatistics]

Not a genius, but glad I could help :)

[@ExactusAtelier]

Here I am as a graphic designer watching a video about expected value yet found it way more entertaining than any business calculus course I took in college. Thank you 😂

[@jbstatistics]

Thanks! Other than 1 year in Georgia, I've lived in Ontario my whole life, and near Toronto for the last 20 or so. But in the last 6 months or so, 4 people have asked me about my accent in face to face conversations. So people are hearing something, but I don't know what it is. I have a tendency to use secondary pronunciations of words that are a little softer than the primary pronunciation. But maybe it's just the small town Northern Ontario Kenora boy showing through :)

[@RenadAdel-og5bs]

this was 12 years ago, OMG, and here I am, reaching out to it 12 years later thank you, man

[@jbstatistics]

You are very welcome!

[@amritsharmapoudel959]

The way you focus on the important points with your voice is just awesome! Likes! You are the real MVP.

[@aditipatil9491]

You made it effortlessly easy to understand 😀 Thank you!!!

[@jbstatistics]

You're welcome Laura, I'm glad you like them!

[@roseroast527]

Thanx man... I'm from India... There will be my exams in 3 days and this question here was the only one from whole probability of our syllabus that I wasn't able to understand... Now u explained it in a really beautiful way...

[@hadidy13]

This is by far the best explanation I've ever watched!

[@jasmeet17mast]

Very clear. Video and audio quality is good too. Thanks for sharing

[@jbstatistics]

+Jasmeet Singh You are very welcome! Thanks for the compliment!

[@jbstatistics]

You are very welcome bugs! I'm happy to help out.

[@BoZhaoengineering]

one of the best interpretation of expected value and variance! definitely.

[@babangidaomolos5104]

what took a semester to understand has been accomplished in less than 8 minutes! amazing....

[@yummymummy123456]

Thank you, it is such a relief to figure this one out. I still have some hair left on my head!!

[@jbstatistics]

+Peta King You are very welcome!

[@applejuice69.]

Im gonna cry KZbin teachers like you make me realize I'M NOT STUPID my stats professor explained this in a way that I couldn't understand at all and i felt like such an idiot cause everyone else seemed to get it thank you SO much!!❤️❤️

[@RononDex35789]

I love you so much. i have been trying to figure out my professors notes and lecture slides for over 2 hours. you are an angel!!!!

[@jbstatistics]

I'm glad to be of help Jim!

[@cyto4335]

11 years later and still saving lives 🙏🙏

[@jbstatistics]

You're very welcome! And thank you very much for the compliment!

[@yoxiyogaming]

This is AMAZING. In this 8minute of video, I learn more than 2 weeks of material

[@jbstatistics]

You're welcome! I'm glad to be of help!

[@426rls]

This is so helpful- you are great at explaining things clearly without moving too slowly. Love your videos!!

[@akinyimildred6012]

I understood it too from Kenya

[@quaemeany]

This is honestly better done than Khan Academy. You seem to know what you're going to say rather than winging it like he does in every single video.

[@jbstatistics]

Thanks Lake. I try very hard to be concise while still being true to statistics. I don't like to waste anybody's time, so I try to keep these videos short and to the point.

[@mjitape2083]

Best Statistics lecture I've ever heard....this is perfect...thank you sir!!

[@TheArnoldification]

Thank you. These videos are very well made and easy to follow. I like my prof but he tends to cover proofs and theory a lot and can be rather difficult to follow sometimes, so these are very helpful for clarification.

[@jbstatistics]

I'm glad to be of help!

[@89Valkyrie]

My professor explains it just like this, just as fast. This is a great refresher. Thank you for the video.

[@kalcivar5]

Thank you, Thank you, Thank you! for your clarification at the beginning of the video! I spent a day trying to understand the book to then watch this video and understand in 8 minutes!

[@Daniel-aaaaa]

I keep looking back at these videos, and there is no better channel than this one. One decade later and it's still high quality. Only downside is that stats and probability is such a broad topic and you're only one person, so coving all of it is impossible 😔

[@parleymanderson7490]

Yeah, I can’t imagine that the 1-and-a-half-hour long lecture from my university can be shortened to 7 minutes and become much easier to be understood.

[@chuckn11]

I just want to say to this guy thank you so much, you really take the time to explain what each little detail means. Ok back to learning.

[@jbstatistics]

You are very welcome. I hope my videos help you learn a lot! Cheers.

[@jianxiongji2578]

i have spent tons of time on this topic and this is by far the most helpful one. Thank you so much!

[@HalorRacer]

If only my teacher could teach like this man

[@HackyTV]

Thanks. This is a great video; really compact and well organized.

[@jbstatistics]

You're welcome! And thanks for the compliment!

[@melindabaye439]

a BIG thank you to JB everything is so clear it is very helpful

[@rishabhnarula1999]

great teaching sir, thanks.👍😊

[@Zoni-arain]

This is so good and I am watching this in 2024.

[@jbstatistics]

Not much has changed in this topic :)

[@Kasun_Ish]

Nice explanation.

[@Satya-chowdhury]

You summed up the full chapter in 7 minutes. And understandable way

[@sssssssssss231]

Excellent teaching,every thing is going straight into head,no doubts at all,thank you

[@faseg1000]

This is a great job. Well explained and cleared all my doubts and confusion.

[@beefandpotatoes6525]

as usual very organized, well explained, and with right speed.

[@timothyr.pachuau4878]

So much more helpful than our lecturer....thank you

[@djcinetic]

Perfect! but how did you find the 0.16, 0.48, 0.36 probabilities? are these just random example values?

[@BasilBabar1]

From the given statement we know that 60% of the people approve the president. In other words probability of choosing a random person who approves the president is 0.6. Conversely, the probability of choosing a person who disapproves of the president is 0.4 - X=0 means that choosing two people who disapproves the president. Therefore 0.4*0.4=0.16 - X=2 means that choosing two people who approves the president. Therefore 0.6*0.6=0.36 - X = 1 means one person disapproves while other approves. Therefore 0.6*0.4*2 = 0.48 ( I multiplied it by 2 bcz there are 2 possible combinations i.e. either the first person approves and second disapproves or the first disapproves and the second approves) The main assumption over here is that choosing a person from the population doesn't change the probability distribution considering the sample size is large. Had it been a case where the sample size was small then we had to redefine the value of probability while choosing the second person. Hope it helps!

[@houston8713]

@@BasilBabar1 goated

[@alena6223]

Thanks for actually explaining things. Makes so much more sense now.

[@jbstatistics]

+Alena Foresterun You are welcome. I'm glad I could help!

[@jbstatistics]

Thanks! I'm glad you liked it.

[@Xorked]

you're awesome dude

[@faustin289]

I enrolled to an inference statistics course on Coursera.org and couldn't wrap my head around this module. Thanks for saving me!

[@Michael_gitau]

In 2025 and its still helpful🥳🥳 i wonder why some disliked it Wonderful explanation 🤘

[@landonchan7429]

TY JB! Ur straight up saving our grades out here. God bless!

[@jbstatistics]

I'm glad to be of help!

[@aymanadam7825]

Thanks a lot!! You explain it way better than my professor in the university.

[@jessicajiang139]

Just want to say thank you. Super easy to understand.

[@jbstatistics]

You are very welcome!

[@chrishoman4521]

great video! understood the work clearly after watching this video.

[@kishore7309]

Better than my professor

[@ng9080]

bless your videos, wow. You're saving me big time.

[@clemiboi]

thanks. you've helped me understand points which i couldnt in a 1.5 hour lecture. more can be emphasized on the meaning of the the expected value and how it contrasts with the actual mean.

[@coreychen3374]

watching this in 2021 before my midterm. thanks jb!

[@garrylove8955]

My lecturer is useless and it's driving me nuts. I did this stuff when I was 16 and somehow he's managed to make it complicated. Thanks for the refresher. Wish me luck.

[@amindehbokri2259]

JB you are my hero for saving me before my exam tomorrow

[@jbstatistics]

I'm glad to be of help! I hope your exam went well!

[@jbstatistics]

You are welcome!

[@wasimsaliby6720]

Great review material for the FE Exam, thanks a lot!!

[@Brinx101]

I love you mister. I've been having trouble with this for hours until i stumbled across your video. Thank you

[@kunbuzo6510]

Thank you sir you are 100x more helpful than my probability professor

[@Leo_Nader]

Incredibly helpful. Thanks a bunch.

[@jbstatistics]

You're welcome!

[@enkapo]

A brilliant piece of work! Thanks!

[@jbstatistics]

You are very welcome. Thanks for the compliment!

[@rajamoorthy1969]

Great explanation. Thanks

[@Anonymous_Pers0n]

Can u replace my lecturer :) hahaha

[@kartikanand5374]

Thanks a lot! Your words were really precise. That helped a lot!

[@nidhimathew9848]

Thank you so much for explaining this so well. This was bugging me for a really long time.

[@beatrixoforiwaahgyimah2571]

Can i ask a question... The part that we were supposed to find the expected value to the question given to us....... Why did u add the x to the px instead of multiplying

[@jbstatistics]

We'd never add x and p(x), that wouldn't ever make sense and I didn't do that in this video. For a discrete random variable X, E(X) = sum x(px). Each value of x, multiplied by its probability of occurring, then add up those terms. I'm not sure what you're referring to here.

[@beatrixoforiwaahgyimah2571]

@@jbstatistics i did check and realised that i made a mistake.... Sorry for any inconvenience caused

[@ramosgv]

Great videos! so helpful and easily understood

[@virnan]

This is done really well sir. You explain in not too technical language.

[@adassyposz3699]

Cheers mate, I'm cramming for my a-level further maths mock, and this has come in really useful.

[@Shelby-cy9vu]

Am I the only one in the comments that's gonna admit I don't understand a single thing going on here. Wish me luck :(

[@evan_-_]

Its oki , how was?

[@amongus8698]

Good luck

[@ysbeautyinc]

This video was so simple and so helpful, great job! Much appreciated.

[@jbstatistics]

Thanks! I'm very glad to be of help.

[@baiqinglyu4254]

This guy is saving my class, can I pay you the tuition instead

[@littlepawwings]

Thank you for this video...I badly needed this method.... thanks a ton.... God bless you

[@jbstatistics]

You are very welcome!

[@NutPae]

Thank you! This video help me understand the whole concept of it!

[@hamayunkhan2287]

Thank you. You saved my life!!!

[@adtkr]

Amazing Narration.... Greatly done

[@jbstatistics]

+A Kr Thanks!

[@rebekahm6672]

Thank you, this made it easier to understand

[@MahmoudAbdo-hb9hn]

thank you❤❤

[@xanderlewis]

Brilliantly explained. Thank you.

[@jbstatistics]

You are very welcome!

[@jbstatistics]

You're welcome!

[@pheonix1461]

Thank you so much for making it easier to understand, my teacher uses a lot of terms that I don't even know what's happening lol.

[@Mbc43m276]

Thanks JB. Would have been impossible understanding this without the video

[@jbstatistics]

You are very welcome!

[@CascadeTwelve]

Really clear and concise. Thank you!!

[@jbstatistics]

You are very welcome!

[@alitahakilicaslan1177]

Thanks for these beneficial informations !

[@lucyfabulous]

How did the “handy relationship” of variance and expectation derive

[@jbstatistics]

E[(X-mu)^2] = E[X^2 + mu^2 - 2Xmu] = E(X^2) + E(mu^2) - E(2Xmu), where E(mu^2) = mu^2 and E(2Xmu) = 2*mu*E(X) = 2*mu*mu=2mu^2, and thus E[(X-mu)^2] = E(X^2) + E(mu^2) - E(2Xmu) = E(X^2) + mu^2 - 2mu^2 = E(X^2) -mu^2. Here I assumed linearity of expectation (which is true), and that the expectation of a sum is the sum of the expectations (also true).

[@lucyfabulous]

@@jbstatistics Thanks a lot！！！

[@jsc0625]

Extremely helpful, thank you!!