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.
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.
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.
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.
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.
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!!!
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!
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
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.
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!!
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.
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 ?
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."
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.
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.
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
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. :-)
@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!
The response you got from Cy Fleming was correct. If you think about it logically with the rain example then, what would it mean if the distribution graph was peaking at 0,9 (y-axis) at 3 inches of rain (x-axis) while considering that the total area under the graph must equal to 1? Naturally it would mean a higher probability of getting *about* 3 inches of rain when compared to say 2 or 4 inches. Thus, the height represents how widely or narrowly the potential values of Y (rain) are distributed.
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
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.
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...
@ 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(
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
depends on your probability function, In the case of rain, it is imposible to get negative rain fall, assumign we dont count evaperation as negative rain fall. So we only have probabiltes from 0 to infanity, So yes it could have an area under a graph of 1 from 0 to 1. In a "Standard" distribution it always equals 1 from -infanity to + infanity. In Quatum mechanics, you can have discrete probabilty functions equal to an area of 1 from -x to x.
So for variables that cannot be negative, like rain fall, how do we / the function take into consideration that part of the distribution which crosses into negative? Is this where we would use log normal distribution?
I could be wrong but I think the height represents how clustered the actual x-values are. For instance, if you have a bunch of values around the same probability (say right around .005) then the graph would be highest around those x-values.
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.
yeah but the 240p is kinda annoying
Sometimes the best content is the vintage one. I still believe that teachers like him are the best teachers that we can find.
yeeesssssss
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.
and now was 15 y.o IM watched this video, and still good for me
KhanAcademy: Saving university students who are disgruntled with their inefficient lecturers since 2006.
I had an introduction to statistics for my Physics course, professor spent 1 hour on this and I thought it was complex nonsense..
wait university? I’m in 7th lol and this helps aha
@@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
@@riccardocapellino9078 lllllll
Man i feel you so badly!
its 2021 and im here before my test, Sal you saving me even more than a decade later
same pappy
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.
this video is so old what
why is it still more helpful than my professor
ig your professor is older than that
This comment is so old what
Why is it more helpful than my professor
@
This comment is so new what
I’m graduated and don’t have a professor
@@Mega88Kat 😱😱😅
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.
+Aldora LaPlume well said
I feel u r ri8
They were probably born after year 2000. That generation doesn't have an attention span unfortunately.
u were born pretty tho, lul.
Omar Farooqui And you shouldn't label people like this too
15 years ago is crazzyy!! 💀💀
I truely love you
love u too
Lol wenn man im Masterstudium zum ersten mal statistik hat und dann Moondye unter dem Video sieht XD
Just liked your comment to make the number of likes 69. I also love his explanation though. :)
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.
how is life going?
EXACTLY 2 INCHES OF RAIN
NOT 2.0000000000000000001
NOT 1.999999999999999999
NOT A SINGLE WATER MOLECULE
Is it a .5 chance?
@@danielniels22 loved this part too much 🤣
@@nocturnalvisionmusic hey thanks for replying my 1 year old comment, it reminds me the day when I first learn stats
@@danielniels22 no problem! Good reminder for me too :D
you save me in every single class!!
Sometimes the best content is the vintage one. I still believe that teachers like him are the best teachers that we can find.
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
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!
A line has no area, and area is required for probabilistic determination. A line (PDF) is a likelihood; an area (CDF) yields a probability.
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.
Agreed, educators are greatly under-appreciated.
This man does more for my education than my professors...
15 years later ma guy still be helping me out.
I hope my statistics professor is going to watch this someday and stop torturing students.
10 years of this video, a petal of thanks from INDIA, this helps me in my GATE 2019 exam
Truly grateful to you, sir! What you explained in just 10 minutes was far better than any of my college or tuition teachers.
Says I don't know upto 10 times in a lecture but knows almost everything that this world has.
@Atharva Kaduskar Nah, Masters' Entrance.
I was in Grade 1 when this video came out. Wow. And now im using it
Just the fact that you make these videos changes how I feel about human nature in general. You are a saint!
60% of the time it works every time
3:15-4:28 is the best part of the video - love that rain specification 😆😁🌧️
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!!!
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!
Thank you, Khan Academy for allowing me to survive college.
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
wow,sal is such a gem of a teacher,great job.
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.
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!!
i probably will get 0 or something tomorrow but i am still watching...
Those who don't understand it, I suggest you to watch the Discrete and continues video. Then you easily get it.
I feel like this should take 1 hour to become a master of, but that is probably just an effect of Khan's explanation.
But what's the probability of it being EXACTLY ONE HOUR OF BECOMING?
@@tedchirvasiu basically impossible to master because of that one darn microsecond.
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.
I love it! Your incredible! I'm studying for exams to be an actuary, and this is helping me immensely.
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 ?
@@skeletonhorse_person Heeey! and you commented this 2 years ago, how's life?
this guy is teaching much better than the lecturers in my class. I feel lucky watching the topic centered tutorials.
These videos brought back fears I had in stats classes!
I find the lecturer very interesting and humorous. Who says Stats has to be boring. Thank you!
You are more than a GOD of teaching!
Thanks for saving my sanity and actually helping me know i am not dumb. The lecturer is the problem not me.😊
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."
I don't understand you
This guy is crazy, There is no one like Sal Khan my god !
This guy will one day win the Nobel peace prize - for changing millions of fates for the better!
Learning from the best teacher in the world..
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.
You rock. I hope you've made lots of money off these. You deserve to.
This is really helping, i feel enlightened when i see this. Tysm
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.
One of the best stats tutorials, I have ever seen :)
I feel enlightened! Really much appreciated and I love your sense of humour. passing CFA L 1 seems so much more realistic now!
people like him don't believe in fate, but he should win some award.
you are a life savior !! thanks sal...
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.
He just cleared my basic doubt and helped me what actually continuous means
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.
Khan Academy still outchea saving lives and degrees!
I want to cry.....................great video.....i wished I knew this before....thank you very very much
its crazy how im 19yo and this vid is here since i was 6, thank you
these videos are great. for some reason my prof like to make the material harder than it actually is!
This channel has the best video on probability
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
Nothing to add, just amazing !!!!
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. :-)
Omg saving my life thank you!!!!!!!!!!
I like how he starts raging at 4:00 LOLOLO.
Me too :D
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
you are 9000 times better than my stats professor.
best explanation i've found yet. why am i not surprised? ;)
@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!
Your clips are saving my college career
The response you got from Cy Fleming was correct. If you think about it logically with the rain example then, what would it mean if the distribution graph was peaking at 0,9 (y-axis) at 3 inches of rain (x-axis) while considering that the total area under the graph must equal to 1? Naturally it would mean a higher probability of getting *about* 3 inches of rain when compared to say 2 or 4 inches. Thus, the height represents how widely or narrowly the potential values of Y (rain) are distributed.
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
11 years later but same! Loved that part too much 🤣
I love this still on 12-15-23 😁😇
My professor made it sound like something crazy but you just explained it so easily. Thank you!
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.
skip from 3:08 to 4:30. 1:30 minutes of counting zeros and why 2 != 2.1
But that's the best part D: :3
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...
casually studying from this video in 2024 lmao
give this man an oscar!
@ 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(
And now P[X=x]=0 for all x in R makes sense for continuous case.
This video is a blessing for learning this topic
Alhamdulillah
Thanks sal sir.
Thanks! for you understand that we understand things better when presented via graphically
Thanks a lot Khan ❤❤❤❤
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
thank you very much.......... a sweet and short lecture......
Most of the people who commented on this video may not be here today.
"Covid"
thanks... cleared my concept!
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
Please post more probability based videos..
depends on your probability function, In the case of rain, it is imposible to get negative rain fall, assumign we dont count evaperation as negative rain fall. So we only have probabiltes from 0 to infanity, So yes it could have an area under a graph of 1 from 0 to 1. In a "Standard" distribution it always equals 1 from -infanity to + infanity. In Quatum mechanics, you can have discrete probabilty functions equal to an area of 1 from -x to x.
No doubt after internet came .. suddenly science got advanced.. cuz now students can understand what someone tryna teach in lectures
really thanks
Thank God you exist.
Totally a life saviour 🙏
I don't know why I gave my university for $42100 1 year instead of this youtube channel.
So for variables that cannot be negative, like rain fall, how do we / the function take into consideration that part of the distribution which crosses into negative? Is this where we would use log normal distribution?
I could be wrong but I think the height represents how clustered the actual x-values are. For instance, if you have a bunch of values around the same probability (say right around .005) then the graph would be highest around those x-values.