"books will show you will just give you a formula..." Literally the reason I am here. Just threw the E(X) at me that produced values greater than one, expecting me to be cool with it and understand wtf the book was talking about. This video cleared everything up nicely!
my teacher doesn't teach... he just writes a bunch of equations, proofs and definitions that no one can follow. i also learn with a bunch of kids that don't voice their concerns out loud, because the culture here is that way. so my frustration level is high because I have to learn everything by myself, and I feel really angry at the teacher.
The culture in many places is that way, trust me. People teach their children the importance of the glory and thoughts of others rather than the importance of knowledge, learning, wandering and exploring. The sad thing is, some of these children are probably going to be teachers.
it's especially bad in asia.. students aren't encouraged to speak up wherein western countries they are. kinda sucks to be lost in class and to do badly on tests when you know you're totally capable of doing well. oh well, life isn't fair sometimes.
My Discrete Mathematics prof is like that. But thats why he doesn't have any grad students anymore. The ones he had all graduated and new ones will either avoid the university or pick another supervisor. Professors get a salary increase if there doing research projects with grad students, no one wants to work with him.
Think it this way. If a teacher tells u every logic behind every math stuff..what would be left for u to use ur own mind. How would u learn to figure it out urself. Do u thing Mr Khan over here had the privileges of excellent teachers. Most likely No. He himself figured it out over the time . But yes teachers in general are boring like that. The best thing a teacher can do is not to tell u every logic behind every formula and stuff BUT encourage u to do urself.
This makes so much sense. I loved the proof behind the E(x) formula. I had no understanding of how this worked, making me very frustrated. Thank you sir.
Thank you so much! E(x) in a previous class has already given me issues. I get caught up in the formulas and it distracts me from the concepts. Watching you explain the connection between the expected value and the population mean made total sense and really cleared this up conceptually for me!
that's maths bro. i'm in 3rd level education studying computer science and at the start i couldn't follow along maths cus it was all these confusing terms being mingled together so i eventually stopped minding the lecturer and just went on youtube where you realize that's everything is easy, it's just the language they use is confusing and in my case unnecessary
"Mathematical average" would be a lot less misleading than "expected value", since it can actually be CERTAIN that the expected value of a random variable won't occur! ("Random variable" is also a misleading term, but we're stuck with it.)
@@Myndir I'm super tempted to go through math using the terms I like. I really like your use of mathematical average here but think "experimental average" is more precise ;)
Y'all are life savers. I have an online statistics class, where the professor has put in ZERO effort. Khan academy is the only reason I'm not failing the course. They're also responsible for me passing all of my math and engineering courses, along with Blackpenredpen.
The concept explaining is really amazing, and much much much better and clear than what written in the book, great course for brush up mind and understand what behind the formular
I'm no math guy and have tried to teach myself statistics out of curiosity using ebooks and stuffs and all miserably failed.. so far I'm enjoying and following to my surprise!
thank you sooooooooooooooooooooooooooooooooooooooooo much................. for 10months i was struggling with this population, sample and expected value . And every thing got solved within 14.52 minutes......... thank you very much.... I wish I watched this 10 months ago;............
I'm cramming for my econometrics class and got so confused with the concepts, your videos just saved me from hours of reading the textbook/reviewing the notes! You're awesome! :)
These lessons are pure gold, and they really show what a multiplicator the internet can be by enabling smart people like you to kick off real revolutions just by uploading their thoughts and ideas and lessons or whatever else is on their mind to the net for all the world to see :-P Sorry, I wish I could express this more eloquently and less long-windedly, but I just want to say THANKS for these videos. And to think that they have been here for close to 2 years and I only discovered them today8-D
If it makes you feel better, studies show that humans are terrible statisticians. It's something our brain simply doesn't get. Which means... we're all in this together.
Lol. It does make me feel better thank you... xD I'm still mad that I have to get a lower GPA than I deserve only for this subject though. Imagine always getting A's since elementary throughout high school and also A's and B's in all other courses at college.. and then comes this pain in the ass with it's big D to penetrate me so hard I forget how to walk through my life afterwards. (All puns intended)
prepareuranus Statistics is actually very very very awesome, one of my absolute favourite courses. BUT (HUUUUGE BUT) it depends on the professor teaching and it depends on how that prof wants to treat the subject. Business school approach to stats is so dumbed down that you actually come out more stupid than you went in. My current Economics prof believes that everyone in the class will become a professor of economics and therefore he treats the entire class as a pure math class where his notes (I'm looking at them right now) are so over-the-top that a normal human being cant understand them: literally, he just writes a proof, then two sentences, then another proof and repeat for 30 typed pages per "chapter." Psychology class however, decided to use words and easily understood examples to explain a concept, then present the formula, then present a more precise formula, then provide a brief on the debate amongst practitioners on different ways to tackle the subject, and done. Thats it. In psych, you understand the concept "Very Well" (not absolutely perfectly to a nauseating level of detail with professor McProof. Prof McProof by the way, makes people despise statistics, makes a few geniuses understand 100% of everything and leaves 90% of the class with a 55% grade and no understanding whatsoever about whatever the hell just happened in that dark period of life. Incidentally, I took Psychology for several years before deciding to go into business instead and then being dissatisfied with how dumbed down everything was, so due to my Straight A's, the Economics department recruited me. I have straight A's in economics also and got A+ in psych stats 1, A+ in psych stats 2, A+ in business Stats 1, A+ in business Stats 2, A+ in Economics Stats 1, and now I am in Economics Stats 2 with Dr.Proof and I don't think I will even pass... why? Its not because I don't understand stats, its because he cant speak fucking english! He can only speak pure mathematics. You ask him a question and he gives you some bs about m^kX(t) = integral [d^k/dt^k e^(tX)]fX(x)dx and then tells you to pop in the MGF for a standard normal variable and I will have my answer... thats what qualifies as an explanation. enga-fuckin-lishhhhhh!!!! Anyways, thats my rant: some people need to learn how to learn stats, but some people also need to learn how to teach stats; because its actually a good and often intuitive subject.
Khan Academy You need a video after this one to tackle Moments and moment generating functions. These topics come up and the notation is deranged so I am sure many would like an explanatory video on that, which is actually good.
Oh! So it's the sum of P(X)n*Xn over n if P(X)n is a discrete probability distribution. It's funny how the illustration here puts this into perspective. Even though my notation may be a bit shaky above the concept is starting to grow legs using the example. If I fumble with expected value in the future my base will be to understand the average, consider a discrete probability distribution, and then apply the average concept to the outcomes using the law of large numbers. Thanks for the breakdown. Feedback: 'd love to see how this example is tied back to the formula in the book to show the connection between this amazing example and the book formula(for future reference)
Your explanation is very articulate. No one ever told me that Expected Value is the other word for Mean of the Population. The more you explain the math the easier it is to understand it. Otherwise we understand it mechanically. However, I expected you to explain and discuss the formula of Expected Values of Random Variables also.
THANK YOU! I'm currently taking a class called Probability and Engineering Application with an absolutely awful professor who can't explain anything, and who wrote a book which is just as unhelpful. Thanks for going over this stuff clearly :)
Hey Guys, help me out here! If you ask me the probability of making one shot, for me I would say p=30%. While saying this, I am actually providing an estimate that I'll be able to make 3 out of 10 shots for sure (means, P(X=3) given n=10 is 100%) But then using same numbers n=10 and p=3 I calculate the binomial probability of making 3 shots out of 10 and it is 26.68%!
Drawing an infinite population is easy: Just set the scale of the axes to increase by powers of 2 while decreasing the distance between powers of 2 along the scale by negative powers of 2. So x = 0 to x = 1 would take 1 space, x = 1 to x = 2 would take .5 space, x = 2 to x = 4 would take .25 space, and so-on, and eventually you will get to a point where an extremely large increment (say, 2^1000 to 2^1001) would take an extremely small space ( in this example, the space between 2^1000 - 2^1001 would take 2^-1000 space ). imply the remaining distances and increments (for feasability purposes) and draw a bound at the edge and call that "infinity". The trick is configuring linear and polynomial functions such that they can be drawn on such a scale.
I thank you thank you thank you a heap for all your videos (right now downloading stats, calculus, linear algebra, and geometry :) ). My current job requires me to pick up those things I learned back in uni (which I have forgotten almost entirely). Thanks KhanAcademy!!!!!!
This is my first year of taking statistics course and until know what I learned was formulas in the book and statistics is the way it is that you just see the formulas without explanation. But of course it did not quite add up there and finally I've found someone here for explanations I am really sorry that people who have to study statistics from those horror books
The most annoying part is the undecisiveness. If you want me to learn a formula just tell me. If you want me to understand the formula then tell me. If you want me to be able to derive the formula let me know. There is a difference between each level of understanding. Society could be so much more advanced if math teachers were more strategic.
No idea why I pay for ridiculous state college tuition, when I spend most of my time watching your videos because you teach better than any of the professors I'm paying. I've been decepted.
We are talking about the outcome of a sample taken from infinite data. In the above example we are looking for head in 6 toss. The expectations will be (0+1+2+3+4+5+6)/7 =3. why we are taking probability in consideration. I want to ask that we find expectation when the sample datat is infinite, but why to look at the complete sample data, we can work on the given data and find the answer
first of all thx for the videos! they are great. now what u showed is actually the EXPECTED VALUE of a discrete Random Variable, which means that the population is countable and not uncountable as u said. To find the expected value of an continuous random Variable (which is the one with the uncountable population) , you have to follow this form : E(X) = ∫ x f(x) dx (the ∫ goes from minus infinity to infinity) ..I m just saying that in case that someone gets confused.
Honestly, I bet that my university teacher doesn't know the meaning of this, thanks for the clarification, I can't imagine myself studying without Khan academy
I understood most of the part but can someone explain we are we multiplying x*p(x) ? or simply like why are we multiplying event with its probability ? what does it signify?
I have a doubt, @12:14 E(X) = 0* 1.563 percent, isn';t it a dice the prob of getting a zero should be zero and not considered here... Not sure, but if someone could please explain. Thanks
Really only in this video i got to know how exp. Is equal to mean intuitively. Can you tell me which book i should follow for this kind of understanding.
Expected value becomes the population mean only if the probability distribution is given for the population right? In this case, to illustrate the concept, only the sample's probability distribution has been taken right? As in, in the case of 6 tosses of coin, the expected value that we found out actually represents the expected outcome in the case of 6 tosses and not infinite tosses right?
There is one thing I don't get: In the video you state that you'd want to use the frequencies to determine the population mean because the population is basivally infinite. But to determine the frequency, again in turn you need a finite set of data to determine the frequency based on that set of data. I personally don't see any other way to determine the frequency. So in turn, you might as well take the entire data set, divide it by the total number of data points and again you have the mean based on that data set. That mean would be the same as determining the frequency based on that data set and then based on the frequency of each datapoint you'd come to the same data set mean. And like you said, you basically always have a sample. But imo this really stretches the interpretation of the semantic meaning of a sample versus a population. Yes I agree, in theory a population is never finite and so a data set is always a selection. But then we are including the variable: time. And in this case IMO the coin toss outcomes can never even be continuous because the possible outcomes are known. Imo an entire available set of data points available at one given moment is the population at that moment. Hence; all residents of a country = population. A variable is continuous if it van take an (for humans known) undefinable number of outcomes. That is how I interpreted statistics and semantics behind statistics. If my interpretation is incorrect and I follow this given information, then I better damn well hope the next videos are going to provide some answers :P
take a cube (dice) with six colors V I B G Y O and assign a random variable 0 1 2 3 4 5.if u throw the cube(dice) then when u find the expected value intuitively every color shuld hav equal expectaion but for violet u wud multiply it by 0 then it becomes 0....but this is not it.....what am i missin??? thanks for ur answers
So if I got 5 heads after 5 tosses, the chance to get a 6th one is 2%, but on the other hand, the sixth toss is an independent one from the previous ones with 50 % chance of getting a head. From that perspective the theory doesn't make any sense, does it?
Christopher Wrobel if you only consider that single independent toss than yes, it’s a 50% chance. But when you consider the entire sample space of 6 tosses, the probability of getting 6 continuous heads changes. the 2% is the probability to get 6 heads in a row while 50% would be the probability to get a single head on a single toss. you can look at multiplication rules that multiplies 50% 6 times to get the 2%
Statistics are hard to learn whene teacher want to teach it as pur math, but statistics aren't pur math, we use It in real life as a way or thinking, statistics are awsome, and maths behind aren't as hard as we can think, every scientist or engineer musts master it.
How does it help when the population goes to infinity? Say instead of 6 we flip the coin for 100 times, then the frequencies will change! You won't get 6 heads only 1.5% of the times, it will be much larger % than that as we're flipping the coin for 100 times! So how does calculation of E(X) help if it changes every time the population changes? What's the use of calculating this arithmetic mean (that is E(X)) which is nothing but multiplication of some numbers?
You are getting confused between the frequency & sample size of the event. Here you should consider outcomes of 100 times flipped coin as population & 6 random outcomes out of them as an event, then the "expected value" of getting no. of heads will be "3". Now this is an expected value, which is most likely to be the outcome. This will hold true for any 6 random outcomes out of your total population.
It's a little hard to distinguish decimal values, multiplications and comas in your videos because of the low resolution. Maybe you could make them more noticeable in the next videos. Please consider that. Thanks :)
What I just cant understand is that if you have a success rate of 50%, why is the probability of scoring 3 out of 6 equal to 31%? ..Shouldn't it be 50% as well? ..Doesn't a success rate mean that you'll score half the number of throws you make, thus 3 out of 6?
How come this calculate the mean of the population as we are using the frequency of the sample data. I understand this but it not seems like that it will help in finding population mean
Hey! GIANT DOUBT.... How come the Expected Value won't be really the "most probable/expected value(s)" in some cases?????? (As said in 14:00 ) How could you interpret as an "Expected value" a non-probable value when it results form having very probable values around it?
If a teacher tells u every logic behind every math stuff..what would be left for u to use ur own mind. How would u learn to figure it out urself. Do u thing Mr Khan over here had the privileges of excellent teachers. Most likely No. He himself figured it out over the time . But yes teachers in general are boring like that. The best thing a teacher can do is not to tell u every logic behind every formula and stuff BUT encourage u to do urself.
Why did the population mean equal out to 3.6, while the expected value equaled out to 3.00, and yet he's saying it's the same thing? Is it because you can't have 3.6 flips of a coin, so you round down?
+Daniel Blais I think he means the expected value is equal to the µ of a theoretical infinite population. Usually the population size is bigger than 6 though so they're usually pretty close. I think. Someone correct me if what I just said is not right.
These videos are 13 years old and yet they're so good, thank you Khan Academy!
This is the best video series on stats. Thanks a lot for making it available to everyone to learn and grow.
"books will show you will just give you a formula..." Literally the reason I am here. Just threw the E(X) at me that produced values greater than one, expecting me to be cool with it and understand wtf the book was talking about. This video cleared everything up nicely!
my teacher doesn't teach... he just writes a bunch of equations, proofs and definitions that no one can follow. i also learn with a bunch of kids that don't voice their concerns out loud, because the culture here is that way. so my frustration level is high because I have to learn everything by myself, and I feel really angry at the teacher.
The culture in many places is that way, trust me.
People teach their children the importance of the glory and thoughts of others rather than the importance of knowledge, learning, wandering and exploring.
The sad thing is, some of these children are probably going to be teachers.
user name checks out
it's especially bad in asia.. students aren't encouraged to speak up wherein western countries they are. kinda sucks to be lost in class and to do badly on tests when you know you're totally capable of doing well. oh well, life isn't fair sometimes.
My Discrete Mathematics prof is like that. But thats why he doesn't have any grad students anymore. The ones he had all graduated and new ones will either avoid the university or pick another supervisor. Professors get a salary increase if there doing research projects with grad students, no one wants to work with him.
Think it this way. If a teacher tells u every logic behind every math stuff..what would be left for u to use ur own mind. How would u learn to figure it out urself.
Do u thing Mr Khan over here had the privileges of excellent teachers. Most likely No. He himself figured it out over the time .
But yes teachers in general are boring like that. The best thing a teacher can do is not to tell u every logic behind every formula and stuff BUT encourage u to do urself.
Wow....
This was the only video I've seen that intuitively demonstrates WHY e(x)=μ
This makes so much sense. I loved the proof behind the E(x) formula. I had no understanding of how this worked, making me very frustrated. Thank you sir.
Thank you so much! E(x) in a previous class has already given me issues. I get caught up in the formulas and it distracts me from the concepts. Watching you explain the connection between the expected value and the population mean made total sense and really cleared this up conceptually for me!
This man is a genius. I think he is the greatest educator on this planet.
Every time he said "i don't know"but he knows everything 😅😅
Wtf?
This is so easy.
I have been dreading this topic for so long.
turns out it's just an average.
that's maths bro. i'm in 3rd level education studying computer science and at the start i couldn't follow along maths cus it was all these confusing terms being mingled together so i eventually stopped minding the lecturer and just went on youtube where you realize that's everything is easy, it's just the language they use is confusing and in my case unnecessary
"Mathematical average" would be a lot less misleading than "expected value", since it can actually be CERTAIN that the expected value of a random variable won't occur!
("Random variable" is also a misleading term, but we're stuck with it.)
@@Myndir I'm super tempted to go through math using the terms I like. I really like your use of mathematical average here but think "experimental average" is more precise ;)
I was out here thinking how moment of order 1 is equal to E(X) when both are arithmetic means🤦♂️
Just different names and different purposes
Very true
Y'all are life savers. I have an online statistics class, where the professor has put in ZERO effort.
Khan academy is the only reason I'm not failing the course.
They're also responsible for me passing all of my math and engineering courses, along with Blackpenredpen.
This is the phenomenal explanation of Mathematical Expectation and the Myu Mean and their composition. Thank you again.
The concept explaining is really amazing, and much much much better and clear than what written in the book, great course for brush up mind and understand what behind the formular
I'm no math guy and have tried to teach myself statistics out of curiosity using ebooks and stuffs and all miserably failed.. so far I'm enjoying and following to my surprise!
Got in class early and watched this before his lesson...
arent you a r6 youtuber
Never in my life would I expect Macie Jay here
This is the last thing i expected
Pro gamer move!!!!
Respect: over 9000+!!!
Very cool!!
Nerd
thank you sooooooooooooooooooooooooooooooooooooooooo much................. for 10months i was struggling with this population, sample and expected value . And every thing got solved within 14.52 minutes......... thank you very much....
I wish I watched this 10 months ago;............
if your professor did that great of a job, you wouldn't be looking it up on youtube. Just saying.
roasted
based
I'm cramming for my econometrics class and got so confused with the concepts, your videos just saved me from hours of reading the textbook/reviewing the notes! You're awesome! :)
These lessons are pure gold, and they really show what a multiplicator the internet can be by enabling smart people like you to kick off real revolutions just by uploading their thoughts and ideas and lessons or whatever else is on their mind to the net for all the world to see :-P Sorry, I wish I could express this more eloquently and less long-windedly, but I just want to say THANKS for these videos. And to think that they have been here for close to 2 years and I only discovered them today8-D
I will never understand statistics. It sucks that it's a fundamental course in Engineering. Fuck this.
If it makes you feel better, studies show that humans are terrible statisticians. It's something our brain simply doesn't get. Which means... we're all in this together.
Lol. It does make me feel better thank you... xD
I'm still mad that I have to get a lower GPA than I deserve only for this subject though. Imagine always getting A's since elementary throughout high school and also A's and B's in all other courses at college.. and then comes this pain in the ass with it's big D to penetrate me so hard I forget how to walk through my life afterwards.
(All puns intended)
prepareuranus Fuck you Doflamingo, calculate the stats of Luffy kicking your ass.
Mia Evans best of luck!
I still can't believe I'm done with it for good, that was a horrible demotivating experience.
prepareuranus Statistics is actually very very very awesome, one of my absolute favourite courses. BUT (HUUUUGE BUT) it depends on the professor teaching and it depends on how that prof wants to treat the subject. Business school approach to stats is so dumbed down that you actually come out more stupid than you went in. My current Economics prof believes that everyone in the class will become a professor of economics and therefore he treats the entire class as a pure math class where his notes (I'm looking at them right now) are so over-the-top that a normal human being cant understand them: literally, he just writes a proof, then two sentences, then another proof and repeat for 30 typed pages per "chapter." Psychology class however, decided to use words and easily understood examples to explain a concept, then present the formula, then present a more precise formula, then provide a brief on the debate amongst practitioners on different ways to tackle the subject, and done. Thats it. In psych, you understand the concept "Very Well" (not absolutely perfectly to a nauseating level of detail with professor McProof. Prof McProof by the way, makes people despise statistics, makes a few geniuses understand 100% of everything and leaves 90% of the class with a 55% grade and no understanding whatsoever about whatever the hell just happened in that dark period of life. Incidentally, I took Psychology for several years before deciding to go into business instead and then being dissatisfied with how dumbed down everything was, so due to my Straight A's, the Economics department recruited me. I have straight A's in economics also and got A+ in psych stats 1, A+ in psych stats 2, A+ in business Stats 1, A+ in business Stats 2, A+ in Economics Stats 1, and now I am in Economics Stats 2 with Dr.Proof and I don't think I will even pass... why? Its not because I don't understand stats, its because he cant speak fucking english! He can only speak pure mathematics. You ask him a question and he gives you some bs about m^kX(t) = integral [d^k/dt^k e^(tX)]fX(x)dx and then tells you to pop in the MGF for a standard normal variable and I will have my answer... thats what qualifies as an explanation. enga-fuckin-lishhhhhh!!!! Anyways, thats my rant: some people need to learn how to learn stats, but some people also need to learn how to teach stats; because its actually a good and often intuitive subject.
Khan Academy You need a video after this one to tackle Moments and moment generating functions. These topics come up and the notation is deranged so I am sure many would like an explanatory video on that, which is actually good.
Your every video shows beauty of maths and encourage us to learn more and more.
Thanks sir and khan academy team for all your support.
You Sir are a GENIUS! I never thought of it that way
Oh! So it's the sum of P(X)n*Xn over n if P(X)n is a discrete probability distribution. It's funny how the illustration here puts this into perspective. Even though my notation may be a bit shaky above the concept is starting to grow legs using the example. If I fumble with expected value in the future my base will be to understand the average, consider a discrete probability distribution, and then apply the average concept to the outcomes using the law of large numbers.
Thanks for the breakdown.
Feedback: 'd love to see how this example is tied back to the formula in the book to show the connection between this amazing example and the book formula(for future reference)
Your explanation is very articulate. No one ever told me that Expected Value is the other word for Mean of the Population. The more you explain the math the easier it is to understand it. Otherwise we understand it mechanically. However, I expected you to explain and discuss the formula of Expected Values of Random Variables also.
I think a more accurate way of saying it would be that it is the EXCPECTED mean of the population. Khan Academy is the best!
THANK YOU! I'm currently taking a class called Probability and Engineering Application with an absolutely awful professor who can't explain anything, and who wrote a book which is just as unhelpful. Thanks for going over this stuff clearly :)
Hey Guys, help me out here! If you ask me the probability of making one shot, for me I would say p=30%.
While saying this, I am actually providing an estimate that I'll be able to make 3 out of 10 shots for sure (means, P(X=3) given n=10 is 100%)
But then using same numbers n=10 and p=3 I calculate the binomial probability of making 3 shots out of 10 and it is 26.68%!
Drawing an infinite population is easy: Just set the scale of the axes to increase by powers of 2 while decreasing the distance between powers of 2 along the scale by negative powers of 2. So x = 0 to x = 1 would take 1 space, x = 1 to x = 2 would take .5 space, x = 2 to x = 4 would take .25 space, and so-on, and eventually you will get to a point where an extremely large increment (say, 2^1000 to 2^1001) would take an extremely small space ( in this example, the space between 2^1000 - 2^1001 would take 2^-1000 space ). imply the remaining distances and increments (for feasability purposes) and draw a bound at the edge and call that "infinity".
The trick is configuring linear and polynomial functions such that they can be drawn on such a scale.
This is superb way of explaining thing, I was looking for it for long time.
I thank you thank you thank you a heap for all your videos (right now downloading stats, calculus, linear algebra, and geometry :) ). My current job requires me to pick up those things I learned back in uni (which I have forgotten almost entirely). Thanks KhanAcademy!!!!!!
Every time you smash the like button, an actuary smiles
Such a rare occurrence. A toaster quality video on KhanAcademy. I'm honored.
This is my first year of taking statistics course and until know what I learned was formulas in the book and statistics is the way it is that you just see the formulas without explanation. But of course it did not quite add up there and finally I've found someone here for explanations I am really sorry that people who have to study statistics from those horror books
The most annoying part is the undecisiveness. If you want me to learn a formula just tell me. If you want me to understand the formula then tell me. If you want me to be able to derive the formula let me know. There is a difference between each level of understanding. Society could be so much more advanced if math teachers were more strategic.
Literally the first time I understood expectation fully.
Great Explanation!
No idea why I pay for ridiculous state college tuition, when I spend most of my time watching your videos because you teach better than any of the professors I'm paying.
I've been decepted.
We were all deceived lMAO
We are talking about the outcome of a sample taken from infinite data. In the above example we are looking for head in 6 toss. The expectations will be (0+1+2+3+4+5+6)/7 =3.
why we are taking probability in consideration.
I want to ask that we find expectation when the sample datat is infinite, but why to look at the complete sample data, we can work on the given data and find the answer
first of all thx for the videos! they are great.
now what u showed is actually the EXPECTED VALUE of a discrete Random Variable, which means that the population is countable and not uncountable as u said.
To find the expected value of an continuous random Variable (which is the one with the uncountable population) , you have to follow this form : E(X) = ∫ x f(x) dx (the ∫ goes from minus infinity to infinity) ..I m just saying that in case that someone gets confused.
Honestly, I bet that my university teacher doesn't know the meaning of this, thanks for the clarification, I can't imagine myself studying without Khan academy
I Expected Value from this explanation, and I got it.
Thanks a lot, everywhere we used to get a formula x*p(x) and we used to feel why multiply it..Thanks for d concept !!
i feel like this guy knows everything in every subject
I see him in math videos, in physics, in chemistry, biology, SAT videos, even in economics videos.
What have i done in my whole life😫
THANKS! great explanations Khan! I love your teaching style
@EMRAlvarez. I believe they were two different examples. The first example being 3,3,3,4,5 and the second being the coin flips.
I played 800 dollars for a stats course, and I'm on TH-cam learning it...
(dat feel when you're an idiot and feel like you've been ripped off)
same
Life saver before my Econometrics midterm.....
Finally I get why E(X)=the sum of x.pr(x) for all 'x'
I understood most of the part but can someone explain we are we multiplying x*p(x) ? or simply like why are we multiplying event with its probability ? what does it signify?
I have a doubt, @12:14 E(X) = 0* 1.563 percent, isn';t it a dice the prob of getting a zero should be zero and not considered here...
Not sure, but if someone could please explain. Thanks
Really only in this video i got to know how exp. Is equal to mean intuitively. Can you tell me which book i should follow for this kind of understanding.
These are helpful but omggggg he turns a topic that could be discussed in 4-5 minutes max into a 15 min long video
thanks for the video it was intuitive that expected value and mean represent same thing but not before you said that
Te n years later this video is insightful
Expected value becomes the population mean only if the probability distribution is given for the population right? In this case, to illustrate the concept, only the sample's probability distribution has been taken right? As in, in the case of 6 tosses of coin, the expected value that we found out actually represents the expected outcome in the case of 6 tosses and not infinite tosses right?
Sal, you are amazing for dis. my proff makes everything way more complicated.
beside the practice on Khan academy, is there any other textbook, PDF or practice downloadable i can take on the web for Math? thanks!
before this video, I couldn't understand. After the video... *sunglasses*... I Khan.
There is one thing I don't get: In the video you state that you'd want to use the frequencies to determine the population mean because the population is basivally infinite. But to determine the frequency, again in turn you need a finite set of data to determine the frequency based on that set of data. I personally don't see any other way to determine the frequency.
So in turn, you might as well take the entire data set, divide it by the total number of data points and again you have the mean based on that data set. That mean would be the same as determining the frequency based on that data set and then based on the frequency of each datapoint you'd come to the same data set mean.
And like you said, you basically always have a sample.
But imo this really stretches the interpretation of the semantic meaning of a sample versus a population. Yes I agree, in theory a population is never finite and so a data set is always a selection. But then we are including the variable: time.
And in this case IMO the coin toss outcomes can never even be continuous because the possible outcomes are known.
Imo an entire available set of data points available at one given moment is the population at that moment. Hence; all residents of a country = population.
A variable is continuous if it van take an (for humans known) undefinable number of outcomes.
That is how I interpreted statistics and semantics behind statistics. If my interpretation is incorrect and I follow this given information, then I better damn well hope the next videos are going to provide some answers :P
best tutorial ever
take a cube (dice) with six colors V I B G Y O and assign a random variable 0 1 2 3 4 5.if u throw the cube(dice)
then when u find the expected value intuitively every color shuld hav equal expectaion but for violet u wud multiply it by 0 then it becomes 0....but this is not it.....what am i missin??? thanks for ur answers
"0" is being used as a name for violet, not a probability.
So if I got 5 heads after 5 tosses, the chance to get a 6th one is 2%, but on the other hand, the sixth toss is an independent one from the previous ones with 50 % chance of getting a head. From that perspective the theory doesn't make any sense, does it?
Christopher Wrobel if you only consider that single independent toss than yes, it’s a 50% chance. But when you consider the entire sample space of 6 tosses, the probability of getting 6 continuous heads changes. the 2% is the probability to get 6 heads in a row while 50% would be the probability to get a single head on a single toss. you can look at multiplication rules that multiplies 50% 6 times to get the 2%
Thank you very much sal .. Superb video as always..
great work..keep it going !!!!!!!!!!
I literally clapped.
My expectation from Khan academy for Expected value got fulfilled.
Statistics are hard to learn whene teacher want to teach it as pur math, but statistics aren't pur math, we use It in real life as a way or thinking, statistics are awsome, and maths behind aren't as hard as we can think, every scientist or engineer musts master it.
Thanks for explaining why the E(X)= np
How does it help when the population goes to infinity? Say instead of 6 we flip the coin for 100 times, then the frequencies will change! You won't get 6 heads only 1.5% of the times, it will be much larger % than that as we're flipping the coin for 100 times! So how does calculation of E(X) help if it changes every time the population changes? What's the use of calculating this arithmetic mean (that is E(X)) which is nothing but multiplication of some numbers?
You are getting confused between the frequency & sample size of the event. Here you should consider outcomes of 100 times flipped coin as population & 6 random outcomes out of them as an event, then the "expected value" of getting no. of heads will be "3". Now this is an expected value, which is most likely to be the outcome. This will hold true for any 6 random outcomes out of your total population.
How can you assert that "relative frequencies of a sample" to be same as "relative frequencies of a population itself" ?
Wonderfull Explanation...
awesome..u just made my day...
Simply awesome...
You Rule! Any plans of doing some modern physics? or even Maxwell's equations. And maybe some curl(curl(an E field))?
It's a little hard to distinguish decimal values, multiplications and comas in your videos because of the low resolution. Maybe you could make them more noticeable in the next videos. Please consider that. Thanks :)
Devore? God I'm dying with Devore's book...
What I just cant understand is that if you have a success rate of 50%, why is the probability of scoring 3 out of 6 equal to 31%? ..Shouldn't it be 50% as well? ..Doesn't a success rate mean that you'll score half the number of throws you make, thus 3 out of 6?
ls600h1..dude the answer would be then be zero...which absolutely makes sense since get a exact no. is impossible...
man...you are a bless
"expected value" doesn't have to be the most expected value :D That's why I hate English :D
yeah. It is more like average value or the mean
Every lecture I zone out. No matter the subject. And every time I come back to, the teacher has drawn a potato on the board. 5:29
Ray Dalio brought me here
How come this calculate the mean of the population as we are using the frequency of the sample data. I understand this but it not seems like that it will help in finding population mean
OMGosh! You explained it so easy! Why can't you teach math at King College? Thank you!
So great!
brilliant, thanks Sal!
i want my math teacher to learn from this
Thank you very much.
seeing as youre paying for him to explain it, I'd hope he'd do a good job.
PLEEESSE make videos for quantum mechanics. This is so close, carries the base ideas, but using them with electrons looses me.
What about a function though. No videos ANYWHERE on that
Sir how to calculate that probability distribution chart
Hey! GIANT DOUBT.... How come the Expected Value won't be really the "most probable/expected value(s)" in some cases??????
(As said in 14:00 ) How could you interpret as an "Expected value" a non-probable value when it results form having very probable values around it?
can we say E(X) = sideways M (i = 0 to n) i * y set i? where y set i is the frequency of i?
If a teacher tells u every logic behind every math stuff..what would be left for u to use ur own mind. How would u learn to figure it out urself.
Do u thing Mr Khan over here had the privileges of excellent teachers. Most likely No. He himself figured it out over the time .
But yes teachers in general are boring like that. The best thing a teacher can do is not to tell u every logic behind every formula and stuff BUT encourage u to do urself.
Great explaination!
im your greatest fan
May god bless you
Why did the population mean equal out to 3.6, while the expected value equaled out to 3.00, and yet he's saying it's the same thing?
Is it because you can't have 3.6 flips of a coin, so you round down?
+Daniel Blais I think he means the expected value is equal to the µ of a theoretical infinite population. Usually the population size is bigger than 6 though so they're usually pretty close. I think. Someone correct me if what I just said is not right.
makes a lot of sense
the spider profile pic is soo 2 months ago...