Probability density functions | Probability and Statistics | Khan Academy

[@avananana]

I don't care that this video is over 13 years old, it still contains more useful and comprehensible information than most formal lectures that you can find at universities and colleges. Khan Academy is a blessing to university students.

[@SuperOtter]

yeah but the 240p is kinda annoying

[@rishabhpandey12aroll7.5]

Sometimes the best content is the vintage one. I still believe that teachers like him are the best teachers that we can find.

[@abebayehuhaile49]

yeeesssssss

[@smartguyray3372]

I'm a current student now taking Statistics and although I was looking for something else, this video just helped me understand what I was working on last week and it's clearer now.

[@rakhadavin1988]

and now was 15 y.o IM watched this video, and still good for me

[@Quarker]

KhanAcademy: Saving university students who are disgruntled with their inefficient lecturers since 2006.

[@riccardocapellino9078]

I had an introduction to statistics for my Physics course, professor spent 1 hour on this and I thought it was complex nonsense..

[@amelialane7150]

wait university? I’m in 7th lol and this helps aha

[@schjo4635]

@@amelialane7150 keep strong at it you will cary it through till the end of university. I didnt focus well when I was your grade and it cost me

[@linalina-tz1tn]

@@riccardocapellino9078 lllllll

[@corradoblondi9792]

Man i feel you so badly!

[@boburnhamsguitar]

its 2021 and im here before my test, Sal you saving me even more than a decade later

[@ahmadsherif8624]

same pappy

[@aldoralaplume566]

I don't know what people are complaining about. I wasn't born smart, and these videos have saved my life, so thank you so much.

[@abhishekbhattacharya7343]

+Aldora LaPlume well said

[@mukund1270]

I feel u r ri8

[@Thefeared786]

They were probably born after year 2000. That generation doesn't have an attention span unfortunately.

[@ghuh1759]

u were born pretty tho, lul.

[@lulusaa7499]

Omar Farooqui And you shouldn't label people like this too

[@Mega88Kat]

this video is so old what why is it still more helpful than my professor

[@tanmay1306]

ig your professor is older than that

[@eNOughPlaY2006]

This comment is so old what Why is it more helpful than my professor

[@Mega88Kat]

@ This comment is so new what I’m graduated and don’t have a professor

[@eNOughPlaY2006]

@@Mega88Kat 😱😱😅

[@Peter_1986]

Sal started studying math at college and at several universities in his early 20s, and since math tends to be really deep at universities it will give you a great understanding for lots of related subjects. Also, Sal definitely seems to understand how to learn and teach very effectively.

[@guitance23]

My tenth video in the Statistics and overall also in Khan academy and I had to now pause it this time and come here to say "Thank You". You explain things very nicely. I like the way you open spaces when you act unsure and also provoke us to think which is good as we get to feel that these notions and certain concepts are just linguistic mappings but the ideas are more than that and they are to be grasped.

[@Moondye7]

I truely love you

[@danielniels22]

love u too

[@MrMw3gamer]

Lol wenn man im Masterstudium zum ersten mal statistik hat und dann Moondye unter dem Video sieht XD

[@sampurnakc]

Just liked your comment to make the number of likes 69. I also love his explanation though. :)

[@078matthijs]

Around 6:00, when Sal began with doing a bit of Calculus, I smiled. I know Calculus because of the Khan Academy!! I know so much because of the Khan Academy. And it makes me so happy knowing that there are superb lectures out there on which I can rely. Next semester I'm starting with Statistics, unfortunately the teacher is terrible, so thank you Sal for these videos.

[@qoxx]

how is life going?

[@ZA-GOAT]

15 years ago is crazzyy!! 💀💀

[@jonowilliams3600]

EXACTLY 2 INCHES OF RAIN

[@danielniels22]

NOT 2.0000000000000000001 NOT 1.999999999999999999 NOT A SINGLE WATER MOLECULE

[@dheerennn]

Is it a .5 chance?

[@nocturnalvisionmusic]

@@danielniels22 loved this part too much 🤣

[@danielniels22]

@@nocturnalvisionmusic hey thanks for replying my 1 year old comment, it reminds me the day when I first learn stats

[@nocturnalvisionmusic]

@@danielniels22 no problem! Good reminder for me too :D

[@hazelgo952]

Yeah I had my doubts thanks to some of the comments but wow, this was heckin useful thanks man!! I finally understand what that integral is for lol To anyone who says they're wasting 10 minutes, just watch it at a faster speed and skip portions you're already confident in.

[@rajshah7734]

Truly grateful to you, sir! What you explained in just 10 minutes was far better than any of my college or tuition teachers.

[@louiscritchie]

I feel like this should take 1 hour to become a master of, but that is probably just an effect of Khan's explanation.

[@tedchirvasiu]

But what's the probability of it being EXACTLY ONE HOUR OF BECOMING?

[@jacktheninja]

@@tedchirvasiu basically impossible to master because of that one darn microsecond.

[@rishabhpandey12aroll7.5]

Sometimes the best content is the vintage one. I still believe that teachers like him are the best teachers that we can find.

[@luiscid8937]

Thank you, Khan Academy for allowing me to survive college.

[@janetkargbo-fc6uz]

There are literal tears forming in my eyes. I’ve been sitting in my probability class feeling so stupid because I couldn’t comprehend this. Thank you so much!!!

[@shashankrustagi5611]

10 years of this video, a petal of thanks from INDIA, this helps me in my GATE 2019 exam

[@kaiar]

I feel enlightened! Really much appreciated and I love your sense of humour. passing CFA L 1 seems so much more realistic now!

[@nocturnalvisionmusic]

3:15-4:28 is the best part of the video - love that rain specification 😆😁🌧️

[@beckyonyekwue9214]

Thanks for saving my sanity and actually helping me know i am not dumb. The lecturer is the problem not me.😊

[@andrewpark1471]

I used to watch this back in high school in 2009. Does the resolution gets degraded over time? lol 240p really? Khan Academy saved my life 12 years ago, and now I'm an engineer sitting in my office trying to remember what probability density function was :'D. Guys, you will need this for reliability engineering if you're ever involved in product development! and there Sal saves my life once again after all this time.

[@thanhhuyenphan9508]

Hi, I'm from VietNam. I'm a student in Vietnam. Thank you so very very very much a lot of with numerous useful lesson.

[@unknowngirl191]

wth this vid is so old and the comments are too xD and it's still so useful thanks for saving my statistics course mate from BD

[@tanmay1306]

Says I don't know upto 10 times in a lecture but knows almost everything that this world has.

[@tanmay1306]

@Atharva Kaduskar Nah, Masters' Entrance.

[@lazarnedeljkovic5615]

I hope my statistics professor is going to watch this someday and stop torturing students.

[@apchaphekar]

I agree with the Nobel Prize comment. I think that is the world's most insightful explaination of a normal distribution curve. i feel blessed!

[@carlamk8348]

you save me in every single class!!

[@japanboy31415]

15 years later ma guy still be helping me out.

[@RollerBGM]

Agreed, educators are greatly under-appreciated. This man does more for my education than my professors...

[@lisaslavick7737]

OMG I am SO thankful for these videos. I was so lost in my biostatistics class. Thankfully my stepson told me to check them out...lifesaver.

[@BoZhaoengineering]

this guy is teaching much better than the lecturers in my class. I feel lucky watching the topic centered tutorials.

[@xaladrez7811]

I was in Grade 1 when this video came out. Wow. And now im using it

[@zukisanimakapela9055]

You are amazing, thanks sir, I'm half way across the world from where you are and your videos are making a huge difference to my learning. Keep it up please...

[@f.dehchar8194]

That moment at 8:30 when it hits you: "From another persons stand of view this looks like shit - a mess made by a kid - but still far more effective than my book in Prob.&Stat."

[@Cube2deth]

I don't understand you

[@rishabhnarula1999]

wow,sal is such a gem of a teacher,great job.

[@rmcgraw7943]

A line has no area, and area is required for probabilistic determination. A line (PDF) is a likelihood; an area (CDF) yields a probability.

[@trainedtiger]

I love it! Your incredible! I'm studying for exams to be an actuary, and this is helping me immensely.

[@skeletonhorse_person]

TrainedTiger Hey how are you ? You commented this 11 years ago, it’s really interesting to me too see a thought from a person that’s 11 years old, how’s life bud ?

[@tasneemahmed3398]

@@skeletonhorse_person Heeey! and you commented this 2 years ago, how's life?

[@Romeowasbleeding1]

LOL! " Not 2.01 inches of rain. Not 1.99 inches of rain, not 1.99999 inches of rain, not 2000001 inches of rain" Gosh I started to get the feeling that he wasn't going to stop! :D

[@nocturnalvisionmusic]

11 years later but same! Loved that part too much 🤣

[@nocturnalvisionmusic]

I love this still on 12-15-23 😁😇

[@vickicharles]

Thank you, You save my life. Three months in stat class and I learned nothing, 12 minutes of watching and listening to you, I was able to comprehend statistic and fall in love with it. Thank You and God Bless you!

[@shutup96]

He just cleared my basic doubt and helped me what actually continuous means

[@brittothomas8614]

wow, just wow.. i am working on learning ML and I am from a non-tech bg, I am at a stage where i wanted to understand what exactly is PDF. I was expecting a vague answer only people mathematically inclined would understand, I was wrong, this make me understand discrete and continuous variables in relation to PDF.. Thank you Khan Academy, now I know here to look for answers that I can understand from ground level

[@nelsonw2096]

Watching this video in Feb 2023 from San Francisco, and again we are happily watching it rain outside after some rough months leading into this winter. :-)

[@mihirkumar2887]

This guy is crazy, There is no one like Sal Khan my god !

[@excelwoman8514]

This is really helping, i feel enlightened when i see this. Tysm

[@brendanrivers]

Just the fact that you make these videos changes how I feel about human nature in general. You are a saint!

[@zaidhamdaan1905]

This video is a blessing for learning this topic Alhamdulillah Thanks sal sir.

[@MrBinitpatel]

Learning from the best teacher in the world..

[@khaleeesi]

Khan Academy still outchea saving lives and degrees!

[@kimikokimi]

My professor made it sound like something crazy but you just explained it so easily. Thank you!

[@shantanudas]

This guy will one day win the Nobel peace prize - for changing millions of fates for the better!

[@katy6470]

I really hate solving , solving is my # 1 enemy in my subjects and then now I'm going to report this topic , it's really hard for me. But thanks to this video. ❤️❤️

[@ivan09182000]

I don't know why I gave my university for $42100 1 year instead of this youtube channel.

[@rohitpingale8774]

One of the best stats tutorials, I have ever seen :)

[@srmcarthur]

Let's all tell our educators that they are appreciated today - tell one teacher or a wise helpful person in our life today how we feel. #TeacherAppreciationDay

[@Xiaorui1016]

This video should be named as 'continuous random variables' instead of 'probability density functions'. Probability density functions are one of two ways to describe the distribution of continuous random variables; and they're the derivatives of cumulative distribution functions.

[@ShahariarRabby]

Those who don't understand it, I suggest you to watch the Discrete and continues video. Then you easily get it.

[@pinkcray0n]

This is amazing because my prof just told us that given points have no probability but he didn't explain why so I was just memorizing facts but after watching this video I see the logic behind these facts!! Thanks!!

[@zhenminliu]

I find the lecturer very interesting and humorous. Who says Stats has to be boring. Thank you!

[@Rsingh1]

Thanks! for you understand that we understand things better when presented via graphically

[@Yaki755]

its crazy how im 19yo and this vid is here since i was 6, thank you

[@VinothKumar-qo7ry]

Thanks a lot Khan ❤❤❤❤

[@KamuzXDriver]

@Cerpin1 Basically any distribution showing you the prob. of a given value of a random variable is a prob. distribution. When we talk about discrete random variables it's called prob. mass function, and when continuous it's called prob. density function. btw, I love these videos, great explanation!

[@danchisholm1]

You rock. I hope you've made lots of money off these. You deserve to.

[@p0k_]

thank you so much, i didn't have a clue how or what these things even were and i have a stats 2 exam in like a month, this video saved my life

[@samaritantajjeb2385]

@ 8:11 you cant calculate the probability P(>4) unless you use limits. In a case like that where there is an asymptote on one side but not the other use: P(>4) = 1 - P(

[@_aft]

I like how he starts raging at 4:00 LOLOLO.

[@nocturnalvisionmusic]

Me too :D

[@ignaitog]

casually studying from this video in 2024 lmao

[@em0vskangoura]

You are more than a GOD of teaching!

[@esmailiyou]

This channel has the best video on probability

[@chatsociety]

These videos brought back fears I had in stats classes!

[@anandw0w]

Omg saving my life thank you!!!!!!!!!!

[@andrewhunter6880]

Omg the rant about the atoms of rain almost ended me.

[@anikakabir9145]

I know right. I was like, I do not have time, just give me the solution.

[@nocturnalvisionmusic]

I loved that part honestly 😂

[@dalecomments]

I want to cry.....................great video.....i wished I knew this before....thank you very very much

[@sharkmentality4554]

Nothing to add, just amazing !!!!

[@10babiscar]

people like him don't believe in fate, but he should win some award.

[@wa9r]

you are 9000 times better than my stats professor.

[@johnnyroc]

The concepts are extremely easy and memorizing all the definitions and formulas is extremely hard. So 50/50 chance I pass my Econometrics class. My professor is useless so I'm all over the web trying to figure it out.

[@yangjocelyn6959]

Thank you so much for the best explanation.

[@TheSevenofMine]

Great video! Finally understood PDF. Didn't have a clue during the lecture at university.

[@ominous450]

these videos are great. for some reason my prof like to make the material harder than it actually is!

[@tharunishadi3980]

you are a life savior !! thanks sal...

[@beebz666]

skip from 3:08 to 4:30. 1:30 minutes of counting zeros and why 2 != 2.1

[@nocturnalvisionmusic]

But that's the best part D: :3

[@rasmuskarlsson2906]

One point nein, nein, nein, nein, nein!

[@jagmohangaarg1687]

+Rasmus Karlsson Irritated me as well.

[@mr.premponvilai9983]

my dirty mind

[@nocturnalvisionmusic]

@@mr.premponvilai9983 don't we all have those :3

[@inflamedwithrage92]

Its sad that we are prescribed such sad books on probability and statistics on an undergrad level,which only serves to complicate things by rigor-izing BASIC concepts like Random variables and density functions.And now I finally understand the reasoning behind it all.Thanks.

[@ashkandv1983]

great and helpful! I should say this is the first or second time that I leave "like " and comment on a video in youtube!!! Ashkan

[@aimanjamil5454]

You're great..👍👍

[@imnumber142]

I think this is the first time I have watched one of your videos where you didn't use all the colors in the palette. And I've watched a lot of your videos

[@WiredWizardsRealm-et5pp]

No doubt after internet came .. suddenly science got advanced.. cuz now students can understand what someone tryna teach in lectures

[@rohaanali243]

GOOD explanantion thank you so much

[@caseycdecker]

You should make a video about density function without calculus for uniform continuous variables

[@usaf1983]

Your clips are saving my college career

[@wahaajali1009]

thanks... cleared my concept!

[@Jub-x6b]

Thanks🎉❤

[@ajamessssss]

Thank you 👍

[@xmljson9716]

Thank you for your teaching, i totally get the key about the Probability density and PDF.

[@sdzuzyf47]

You are doing such a great job. But one opinion, get a sketch pad, those things a graphic designer will use to substitue mouse. Words would look much better.

[@HuyTran-eb3ch]

you are literally saving me from my lecture... he takes 3 hours just to explain a quarter of the lesson but no one in my class understands...

[@tusharsalunkhe7916]

really thanks

[@dobraOsoba]

best explanation i've found yet. why am i not surprised? ;)