The Expected Value and Variance of Discrete Random Variables

[@RubenAlvarezMtz]

It is cool to have Khan Academy, 3Blue1Brown and all those content creators but sometimes you just want something straight to the point, thank you JB

[@FPrimeHD1618]

Great video man. I'm a math major and find probability 10000000 times more confusing than any course I have taken lol. It doesn't help that our professor only has one tone to his voice, lol. Always nice to have a clear explanation of this material. Thanks!

[@jbstatistics]

+FPrimeHD You are very welcome, and thanks for the compliment!

[@arkamkhan7691]

Lol

[@JimbobFaz]

Ditto.

[@yusuffarah351]

I took so many stat classes at some point even tutor others, but never come a cross some one who can clearly explain this counter intuitive subject. Indeed, knowing a subject and teaching others is too different things. Thank you sir for sharing your knowledge to the world. As some one who love to learn and teach others , I am very grateful to find your videos.

[@boogeythegorilla7330]

Months of missing classes and procrastinating before WACE exams has led me up to this point. Thank you so much!!!

[@AmatisoveLove]

Watching one of your videos makes me understand ten times more than reading the textbook, and your content is better than any other statistics-related videos on youtube. Thank you for uploading this and helping me pass my exams!

[@jbstatistics]

Złotowłosa Panda You are very welcome. I'm glad you've found my videos helpful!

[@jbstatistics]

Złotowłosa Panda You are very welcome. I'm glad you've found my videos helpful!

[@poetryflynn3712]

Marry me please

[@tarehjernetarehjerne4082]

Thanks for this amazing video. Clear to the point and very informative. I dont get why lecturers are unable to meet the quality of free KZbin content

[@the_big_al_01]

I'm so lucky to be in your Stats course at Guelph! Best stats prof out there!

[@GoodLuckForever-wi9kb]

Best Of Luck Forever For Sharing Such a Deep Knowledge in such a simple way. Well Done Sir

[@hellfirelordofevil]

Your exposition of the subject is clear, consise and elegant. Thank you very much for producing this invaluable content!

[@jbstatistics]

You are very welcome!

[@zaidsada6841]

You have a knack of keeping confusing topics very simple. You got a new subscriber and a fan !

[@markstephan5492]

Awesome video thanks for posting. I was very confused when my text book showed E(X-E(X))^2 but you explaining that the second E(X) is the mean "μ" was a huge help.

[@goodknight3072]

Good presentation, likable voice, understandable English, clear explanations, good stuff.

[@abdiraheemabi5021]

I rarely take the time to comment let alone like the video, however this video was by far the best I have come across.

[@ptliang011]

THANK YOU! PLEASE MAKE MORE VIDEOS LIKE THIS ON OTHER SUBJECTS!!! YOU ARE A GOD!

[@jbstatistics]

You are very welcome.

[@ptliang011]

jbstatistics No seriously, please make more. I saw that you are a stats professor. Can you please make some in this concise format about mathematical statistics? Like show some proofs for these theorems? Can you make some videos on other branches of mathematics like real analysis? Or a video on how to do proofs? Your videos are of higher quality than Khan Academy's. Seriously, this is the clearest explanation of this I have ever seen. Please, please make more videos! Please help us students out. Thank you.

[@aria213312]

Thank you sir, you are explaining almost every material that my prof is covering.

[@jakeholdroyd193]

Really well put together videos, im refreshing my brain before going back to uni and this is doing the trick nicely, thankyou for making these.

[@jbstatistics]

You are very welcome Jake. Thanks for the compliment!

[@rohanmore1774]

Has somebody ever told you how awesome you are ? If not lemme tell, you sir are great at explaining !!!;)

[@jonathanm.5066]

Thank you very much for continuing to post statistics videos!

[@gwineafowl6946]

very helpful, even almost 10 years after upload! thanks

[@CharinKarashnikov]

This video helps me to understand far much better than 3 hours statistics class. Unluckily, found this just only a night before test. 😔

[@maorazoulay]

finally got it! Book+ professor did such a lousy job explaining this, i'm so grateful!

[@jbstatistics]

I'm glad to be of help!

[@adrianlindsey2701]

These videos are concise and excellent. Thank you.

[@jackyli1891]

Love your videos you explain everything so well

[@jbstatistics]

Thanks Jacky!

[@michellerayeonpark7142]

Seriously, you are the BEST

[@jbstatistics]

Thanks!

[@valeriereid2337]

Excellent! Thanks for this lecture.

[@takeshi0229]

Great video! How did you calculate E(X^2) = 1.92?

[@starsaverify]

life saviour!! So much better than my nus prof....

[@sushmitanigam4979]

i am grateful to u for providing such an awesome explanation.

[@jbstatistics]

Thanks for the kind words!

[@lamiahsb6628]

Hi, I would like to thank you a lot for making it possible to me to understand probabilities and I wish that you can make videos about how to solve statistics problems by giving us tips how we can understand well a problem and solve it. and thanks again, your videos are really helpful

[@emptyxnes]

Do you happen to have the link for the video regarding @ 3:50 (handy relationship)? thanks again.

[@firefoxyouth]

You Sire deserve an Oscar, although the probability is very low to receive one.. :)

[@jbstatistics]

I agree with your probability assessment :)

[@souravagarwal5945]

thankyou so much , made my life easy, GOD bless you for helping, keep uploading brother.

[@sivakumar-vn7ex]

Bro.I have a doubt ,how did he simulate 1 million values?

[@manasviemmadi8072]

Does it mean that during calculating relative frequencies and carrying out the experiment, the 60% jaundice/heads is preserved and performed accordingly? Or this can be done only for

[@anika_ara9363]

wow!! you were outstanding ya! I understood every part of it but I wish you enlist some related exercises in your website to practice,that would be really helping

[@jbstatistics]

+Anika_Ara Thanks Anika, and thanks for the suggestion. I have many exercises with full solutions that I intend to post at some point in the not-too-distant future. All the best!

[@anika_ara9363]

okay waiting for that :-D

[@romanrobinson1860]

At 4:27, the example to be worked out is different from the explanation given after. I am not so sure why. Can this be resolved?

[@fatimakashefi4312]

worlds of thank you, literally saved my life

[@kimberlin6568]

Thank you thank you thank you! It finally clicked for me!

[@jbstatistics]

You are very welcome!

[@rfconnor3887]

Where could I find the proof the relationship at 4:22?

[@sfaabz]

kzbin.info/www/bejne/nYe5qoOwq797eZY

[@七七-k1x]

Thank you so much and you explained those concepts very well!!

[@spectator5144]

6:58 what would be the R code to generate this simulation? thank you

[@DiddyVonDiddy]

Thanks for the incredible videos! I've been using them to study for my exams. Do you cover joint probabilities in any of your videos? I looked for it but maybe it has a different title. thanks again!

[@jbstatistics]

+DiddyVonDiddy I don't have anything on joint probability distributions yet. Best of luck on your exams!

[@nm800]

I have two questions: -I read that the variance is how much the data are spread, how much the probability space is filled with different probabilities. Is that right? Does it have to do with dispersion? - Why do we square these values? Why is sigma squared?

[@sihlemdziniso3715]

your videos are easy to understand but please include all the calculation

[@spencerprice1676]

Love these videos, can you explain why you might want to square x @7:43

[@yangxiang9933]

since it might be useful to use when finding variance (var=E(x^2)-E(x)^2)

[@parthi2929]

2:10 But why that multiplication? You could have given the background there.

[@mohashyunis5280]

Thanks so much sir, Very clear understanding.

[@jbstatistics]

+Mohash Yunis You are welcome! I'm glad to be of help.

[@KiranAshraf-pf6zt]

Nice explanation sir

[@sawaizniaz1034]

Best One😍😍😍😍

[@sohail2318]

excuse me sir, do we calculate expectation for given range of random variable asked or we calculate for all the possible out comes? for instance if we are asked to find p(2

[@aizeckmwangonda4829]

Sorry how can get P(x)

[@asishcodes]

your videos are great!!

[@delta_kh6608]

I just say THANK YOU!!!

[@koby9340]

One question please I don't get it why segma squared is equal to expected value shouldn't it be segma squared equal expected value divided by N the number of element in a population

[@ujjwal4065]

Really helpful video . nice video.

[@a.m2490]

YOU'RE A GOD DAMN HERO

[@AJ-et3vf]

Awesome video! Thank you!

[@dunethchadeera5838]

Very useful ❤️👍

[@Ali-Ezzat]

On man I don't know what to say Thanks so much Oh BTW where can I find a good illustration for relative frequencies?

[@zyadalharbi180]

thank you very much. very helpful.

[@jongken3725]

very helpful!much thanks

[@halimahabdulbaki5149]

hello, pls can someone help me out with how p(x) was found.

[@estherowusu-ameyaw7781]

Please I had 1.92 for the expected value. Can anyone please show me where I went wrong?

[@rahulpatil6568]

1) E(X^2) is greatherthan equal to (E(X))^2 or 2) E(X^2) only greatherthan (E(X))^2 i m confused.... which one is RIGHT...

[@jbstatistics]

E(X^2) = (E(X))^2 if and only if Var(X) = 0. Var(X) is only 0 for a degenerate distribution, where X can only be a specific constant. In any distribution where there is any variability at all, E(X^2) > (E(X))^2.

[@senpairalemneh9648]

thank you!!!

[@jbstatistics]

You are very welcome!

[@normanremedios8190]

Almost perfect, if not perfect.

[@ajshaka3212]

Awesome vid

[@jbstatistics]

Thanks!

[@aizeckmwangonda4829]

How can get P(x)

[@koketsomokoditoa3255]

thank you- helped a lot

[@vansikasingh3228]

thank you so much!

[@seemaalsaidy6093]

Thank you.

[@Anu_Tuvs]

THANK YOU!

[@AmeerHamza-mt5lm]

Great Sir

[@bleepbloop7768]

why is the p of 1 child having NJ or JN = 0.48 ? wouldn't it be 0.096?

[@ravidwivedi6648]

Records show that 30o/o of all patient9 admitted to a medical clinic fail to pay their dues and eventually their bills are for￾given. Suppose four patients represent a random selection from the large set of prospective patients served by the clinic. Find the probabiliry rhat ; (, all patient's bills wilt evenrually be forgiven (ii) at least one patient bill will be forgiven. Is there anyone who can make me understand what the method to solve this. Help Will Be Needful. TIA

[@SimersTO]

Thank you!!

[@jbstatistics]

You are very welcome!

[@muratderekoylu4673]

thank you sir

[@jbstatistics]

You are very welcome.

[@tawseeftaher9109]

math 4:26

[@bhargabsaharia6361]

very helpfull

[@jbstatistics]

Thanks!

[@ahmalkadumas4539]

amazing

[@mdsamiuzzamanreal3504]

sir thanks

[@lluismontalat4040]

legend

[@thecoolgamer4842]

You make me wanna cry ur voice is so mono toned

[@841533356v]

wow nice

[@jbstatistics]

Thanks!

[@nurulnabilah6941]

🎉

[@shrimatkapoor2200]

Is this guy from Khan Academy Physics cuz he sounds like the same guy

[@jbstatistics]

Nope. I've never been associated with the Khan Academy in any way.

[@ChildMonica-b1z]

Hall Frank Clark Thomas White Scott

[@alex-my8hp]

god damn your good!

[@MohammedAB2030]

The English language is so confusing

[@OfficialTurkz]

nadugo utak ko

[@someoneunknownnn]

Ye oswal ki book yahan kyu le aaya 😭

[@mkosiba79]

Say that again...

[@farouk5344]

Exam is tomorrow, wish me luck ?

[@jbstatistics]

Best of luck!

[@kevinloones5395]

[@raqx9]

bro u deserve my house not just a like

[@anika_ara9363]

wow!! you were outstanding ya! I understood every part of it but I wish you enlist some related exercises in your website to practice,that would be really helping

[@anika_ara9363]

wow!! you were outstanding ya! I understood every part of it but I wish you enlist some related exercises in your website to practice,that would be really helping