Chi-square distribution introduction | Probability and Statistics | Khan Academy

[@sophieyuan1105]

9 years later students are still being saved by this. Super grateful!

[@toyinamunigun2043]

I swear

[@niizumashiiori6402]

it's true...

[@dryrain2]

Make it 10 years later!

[@mylesarsenault9016]

@@dryrain2 make it 11

[@OryxTheDragon]

12 years now.

[@andrewtataj497]

dude, your math videos are the best ones I've found. My prof is awful, I'd be lost without these.

[@gran6782]

That is, by far, the most intuitive explanation of the Chi-Squared distribution I have seen in these past 8 years studying statistics. The definition of chi squared as the sum of squared normally distributed RVs is just genious. The moment he explained that, I was finally able to underdtand why we have so many different curves for each degree of freedom

[@MutantNinjaFly]

My stats teacher just throws a bunch of formulae on the board, and then when you have to do stuff I have no idea where the distributions come from or what they are used for, how to use them, or what they mean.

[@salilbane2675]

Lol

[@meno2739]

Holy crap You wrote this message 9 years ago when and I have to say, things don't change...

[@sanketnawale1938]

I am curious what are you doing now after 9 years.!

[@Ryan라이언]

I can't agree more ROFL

[@sisca8536]

this is exactly what my teacher does, things dont really change even after 11 years 🤷🏻‍♀️

[@lamvo21]

12 years later and still useful!! Thank you so much

[@MASTER3XPL0D3R7]

Thank you so much. My university lecturers aren't great, and I just can't learn maths from a textbook. It helps so much that you have explained it in such a simple, clear way.

[@ShivamRaj004]

How's your maths now?

[@akshaykulkarni3208]

Khan acadamy to the rescue.. Love it

[@camadamsuk]

I love your videos Sal, the one concept I still dont understand is degrees of freedom. i understand what they do but not what they are. I think you explained them at one point but i couldnt find the video looking back through the playlist. maybe dedicating a video to df would be helpful for other statistic students as well. thanks!!!

[@vasishtapolisetty639]

Coming back after 10 years. Thanks Sal!

[@Newbiefly7698]

At 04:45 please explain how a probability distribution sample has a probability of greater than 1 in the chi square curve for k=1?

[@mitchjohnson4714]

This is such a great video. It's amazing how much great information is conveyed in such a simple and succinct way.

[@kowtharhassan882]

The key in teaching stats is to use examples and not just terms so instead of saying variable X it would be better if u did indeed use a variable like weight, height, or anything else so we can follow

[@hassanxami6527]

Still watching it in 2023. He helped everyone

[@蒋俊杰-x6v]

I’m from 2024

[@norwayte]

Could you record a video about degrees of freedom?

[@sumiatheangel9397]

This guy's classroom probably has more A's than an Energizer factory. ~Reus Vult Ave Sumia, Pegasus Breeder and Root Beer Connoisseur

[@Onetime4justice]

Unlikely, for most colleges, there is an implied rule that most students will not get an A.

[@navedkhan4057]

Great video!!! just wanted to understand why do we square X1 and X2?

[@phamdung3884]

Thank you so much! This is THE video that really taught me the concept of Chi squared distribution.

[@noueruz-zaman7894]

lol its called ki-square ..and I have been calling it Chi-square (like chili)

[@lyannamormont298]

Same here bruh😂😂😂..you can't imagine the embarassment i felt after finding out

[@editsjag6160]

Actually it should be pronounce chee, not ki. The letter is chi, it is greek and that is how it is correctly pronounced. Same with pi, it should be pronounced pee

[@glaswasser]

our teacher usually says "guy square" :D

[@superpeaceloveunity]

I'm lost right from the beginning. I'm using the Pearson book for stats class and I think it takes a completely different approach to the chi-distribution. It isn't close to being clear to me yet.

[@yiklongtay6029]

I am too stupid for this.

[@glaswasser]

my thoughts everytime I study something math-related lol

[@chandakabwe5994]

😂😂😂😂😂😂😂 really

[@eseemuraye1230]

I am currently in my Statistics class, waiting for my Professor to finish his lecture on Chi-test (which I don't understand by the way and feeling dizzy) so I can come back here to get the real lecture

[@Catalonia]

I'm a bit lost.. is there a preliminary video to this? I don't know the language.

[@tebellomokgomole772]

I can't believe this. How come I understand, all this time I only understand now. But how. Thanks Khan

[@mpalin11]

A very nice video, I have a statistics course now, this was really helpful! Thank you!

[@StanleyMT]

Im not sure I understood much from this explanation. I would have prefered a more practical application. Could you indicate if you have another video. Also as it relates to the degree of freedom I was a little confused as I thought it was n-1 but you seem to suggest its = to n

[@tvvt005]

6:36 the various standard normal variates come from different normal variates right? Cos otherwise they would be the same right?

[@noortjeburg4504]

Thanks! Never had a class for this subject but now I understand it all!

[@jonasherman9195]

I am pretty new to Statistics, what is the use of a chi-square distribution, based on what I have seen a question could be: What is the chance that it is under this value or is this chi-square distributed.

[@tonimatasnim]

I love this guy.

[@diegoguzman6004]

You are a magician man, thank you!

[@sgdrifter]

it will be better if the origin of these terms (motivation of creation of these terms) are explained in advance of these tutorials. anyway, these tutorials are great :)

[@DumboSanchez]

I'd be lost without these videos man many thanks!!

[@themagniranthine]

Why do chi-squared distribution and chi-squared test have different formulas? Please answer, I'm going to have a presentation tomorrow 🙏🏿

[@pmactwins2]

When the probability is .3, that gives us the value at 2.41 … but aren’t we looking for values greater than 2.41? I think I’m misunderstanding. I would think the answer would be .3 if the question asked P(Q2 ≥ 2.41) … but since we’re strictly looking for values greater than 2.41 I would think we would move up one box … can anyone explain?

[@aldezmail]

His handwriting is great with the mouse, he must be awesome at shooters, HEADSHOT HEADSHOT

[@vivekmittal7893]

aldezmail he most likely uses a digital pen.

[@cc32001]

@@vivekmittal7893 Probably right, but I trip out the whole time I'm watching him thinking what if he was writing with a mouse. The thought distracts me the whole time.

[@hongkyulee9724]

Thank you for the nice video :D This video is really helpful!!

[@mistyshawn4066]

i can pass my exams because of you..thank you so much!

[@marcoskano4437]

13 years later and here I am, finally my turn to watch this for an exam 🎉

[@Trackman2007]

So standard normal distribution is normal distribution's z-scores distribution?

[@sherlockholmes882]

Thanks for visually explaining what this distribution means!

[@petrhorak931]

Khan is my hero.

[@sharonchetia54]

I am really confused with the degree of freedom . I know that formula is : Number of independent variables- Number of constraints. Is degree of freedom 1 when we consider 1 variable because it is an independent variable and we are not doing analysis involving a constraint?

[@lagoscristiam]

Thanks for the videos, what software is he using? Excel?

[@HL-iw1du]

Khan is so smart.

[@pricillajeyapaul]

Does chi-squared distribution formula is E(X)=k, V(X)=2k.? Correct me if this wrong.

[@ayush612]

Awesome Explanation Sir!!! Thanks for the valuable knowledge !

[@Josiah_Cornett]

So, I'm studying for Actuarial Exam P and in a sample exam i'm taking, there is a time when I have to just somehow know that the sum of two squared standard normal random variables is exponentially distributed. Well, more precisely, I"m asked to find the moment generating function of (X^2 + Y^2) / 2 where X and Y are distributed N(0, 1), but in the solution they just throw out there that "Obviously" X^2 + Y^2 is exponentially distributed with hazard rate 0.5 and mean 2. I just don't know how they know that. Wouldn't it be easier to use that this would be Chi-squared?

[@eXcelMathS]

you can prove by joint pdf of X and Y, and switch to polar coordinates that sum of squared standard normal random variable is exponential distributed. It all depends on how the questions are phrased though

[@Joske369]

thank you, that helped alot for my exams

[@VelMurugan-me3xh]

Thanks for this video

[@K1312-s8d]

For degrees of freedom, why are we not applying the rule of n-1. E.g. If you take a sample of 1, you are saying the df is 1 but should it not be (1-1) 0?

[@eXcelMathS]

the rule of n-1 is applied supposingly when X ~ N(mu, sigma^2) where mu is unknown and you use the sample mean to estimate. Because mu is being estimated it takes away 1 degree of freedom when doing chi square test. By the way in this case X has to be converted to standard normal first because it is not.

[@nicolechong620]

it's useful, thanks so much.

[@Xercaas]

Excellent, very instructive

[@maxwellgordon3739]

Maseno University Kenya super supportive

[@DK-ek9qf]

Thanks a lot

[@2pizen]

really great videos!! keep up the good work!

[@mrak8948]

Thank you

[@JelinekFS]

Actually this introduction vid seems to be the only of your chi-square vids I´m having a hard time to understand haha. I guess I shouldn´t have skipped the basics.

[@feel2founded]

Great video! Actually all your videos are really helpful and make things understandable and even intuitive in a way :) Thank you!

[@xojessie75xo]

I am currently taking a biology class, and one our EXTREEEEMELY DIFFICULT assignments is 'Chi Square Test and Corn Genetics Lab'.. I am sooooooo lost!!! I have absolutely NOOOOOOOOOO idea what to do! PLEASE HELP!!!!!!!!!!!!

[@joshuafancher3111]

Great explanation!

[@jessstuart7495]

You forgot to normalize the new chi-squared distributions. You need to make sure the multiple integral ("volume") under the multivariate probability distribution is equal to 1.

[@mar8014]

Sal's VOICE gives me CONFIDENCE.

[@nO_d3N1AL]

great stuff as always

[@Tweeteketje]

You're the best!

[@Joske369]

ur a hero

[@Nickiller6969]

ur awesome mate

[@peuchi1602]

How does this distribution approach standard normal distribution (mean = 0) as df increases if the mean is increasing? Isn't it just approaching a normal distribution (not standard normal)?

[@KMED-gc7gv]

yes, it won't be standard.

[@eXcelMathS]

when n tends to infinity, by central limit theorem, it approaches standard normal.

[@marcwittkowski5146]

I have absolutely no concept of what you could possibly mean by degrees of freedom.

[@julianbenegas512]

How is sigma squared = sigma??? I thought (and been taught always) that standard deviation (sigma) was the square root of the variance (sigma squared)

[@memski9565]

My professor is all good...but I'm here since I was dumb enough not to listen in class

[@medielijah]

why is it that P of Q2 greater than 2,41 and not SMALLER than 2,41??? I do not get how he got to that conclusion

[@natrajtarnalli5903]

Can you explain what exactly X and Q are in real experiment.. may be with some example!

[@eXcelMathS]

X is just a random variable sampled from N ~ (0,1), while Q is X^2 in which X is randomly sampled standard normal random variable

[@yasminfatima5948]

@@eXcelMathS Why the degree for freedom from first sample distribution is one and so on?

[@sanjeevghimire9459]

Good

[@hikarisai7755]

What's the degree of freedom?

[@16jrsoccer]

You're the bessst

[@Mandee1310]

how do you know the degrees of freedom?

[@hseager]

number of parameters you are estimating

[@mitchellkoenig1540]

it should be n-1 and not just n as he makes it appear in this video

[@eXcelMathS]

it depends on number of X you have, and number of unknowns you are estimating.

[@workh4rd]

yeah, i thought he was writing with a mouse too. but from the writing style, i think the mouse is very likely to be made in pen shaped.

[@kvamshi4561]

😂😂

[@johnmandrake8829]

Not all heroes wear capes

[@qjim16]

Try to draw one of those graphs. Khan can't do that.

[@sjsawyer]

Damn it.. my x's looked like chi's to begin with!

[@choice_architect]

Although derived from one another, standard deviation isn't the same as variance. It's true that variance is the measure of spread of the data around the mean, but it by itself can't be interpreted. If we take the square root of the variance, we obtain the standard deviation, which is what we see when we look at spread around the mean in the normal distribution. In the case of N(0, 1), the population mean is zero and its variance is one; the square root of one is one, so our standard deviation becomes one. If we have N (0, 2), however, then we have a mean of zero and a standard deviation of ~1.41.

[@mitchjohnson4714]

I think he was just talking about when the SD is 1.

[@bellybooma]

I love Sal

[@Mike_elGreco]

When I first see the of chi-square in English I thought was something chinese pphrase

[@d.a.d3513]

After 11 year

[@johncharles3907]

so wat the hell is it used for?

[@junmingzheng7456]

so that's where the square coming from??????

[@lifewithdylan]

amen

[@tsunningwah3471]

sdks

[@sakshiigiri7]

👏

[@sarthakthakur87]

😭

[@Zurh1994]

Chi-ote XDDDDD

[@lactigger619]

k-1

[@tausifraza6910]

This teacher is really confused