An Introduction to the Chi-Square Distribution

A brief introduction to the chi-square distribution. I discuss how the chi-square distribution arises, its pdf, mean, variance, and shape.

[hounamao]

the saddest thing is that I understood in 5 minutes what my professor has been trying to explain for forty five minutes. Thanks a lot!

[HenrikANilsen]

It is nearly critical to pace the video in such a way that the viewer has time to grasp what's being presented. Especially when studying scientific subjects with way to much information, without focusing on the students intuition. I found your video to be excellent. Thank you for clearing up my understanding of this distribution.

[krishgoogol]

I have watched lots of vedios to get the base of this topic but none of them were helpful, thank you so much sir u have taught it just <5:28 min ❤️❤️❤️❤️❤️❤️

[cassidycortez]

Fantastic video! Loved the graphic where you compared graphs of different Chi-square distributions with different degrees of freedom. Very insightful and so helpful!! Thank you!

[tigeruppercut]

Is it due to the Central Limit Theorem that the chi square dist appears to look like a normal distribution with larger degrees of freedom?

[serkanhocaoglu]

This is a quite good video with one thing missing, the problem. Which problem does this distrubution help us to solve? Why do we need it? How and by whom was discovered in historical perspective?

[cyrilgarcia]

Can you do one on the gamma distribution?

[sakifzaman]

what if the df = 1, can we interpret it as the distribution is skewed to the right? secondly, for mode you mentioned df atleast 2 may be to deduct it with - 2. so what if df is 1?

[oleersoy]

Ha!! I agree with Houna Mao! This is an awesome video!! Thank you!

[muhammadsalar]

what do you mean by 'degrees of freedom', . you gotta explain that first I believe

[wilsont]

How does the equation in 1:32 suddenly come about?

[sdsa]

Thanks from a curious beginner... just wondering which software uses tables and which ones use algorithms to do the definite integrals of pdf (ie get the area under the curve)... also wondering about non-standard normal distributions... is there a pdf equation for chi-square that includes non-standard normal distributions, ie N(0, 2)... or N(3, 4) or N(-3, -2)?... how about any other distribution? I am under the impression that chi-square is only for standard normal distributions.... is this true?

[patrickkim]

Doesn't the chi squared distribution have k-1 degrees of freedom?

[prinuprince]

Then what will be the mode of the chi square distribution if mean is given

[sudharshanr]

Thank you so much for the amazing explanation🤍

[patsychan]

For k=12, why the max pt located at 12-2=10? Is there any equation?

[PD-vtfe]

Great job. It helped me a lot. Thank you!

[musicmakesmelosecontrol]

The difference of two independent normal variables itself has a normal distribution. Is it true that the difference between two independent chi-squared variables has a chi-squared distribution? Explain

[jamesfilosa]

2:58 ... What's the interpretation of the pdf being greatest at zero for df of 1 and 2?

[alirezasaberi]

Dude you are amazing! keep the great work up :)