18: Chi Square Proof

More detailed explanation of why we use chi square for sample variance.

[abdelrahmanshehata]

I've been looking for that explanation for too much time,
Thanks a lot : )

[statistician]

This proof is very close, but the reasoning isn't quite right. You are missing one crucial step toward the end of your proof. You can't simply determine that (n-1)S^2/sigma^2 is Chi-squared n-1 by subtracting the Chi-squared 1 term from the Chi-squared n term because you haven't proved the independence of those two terms. You must show that the term containing S^2 is independent from the term containing Xbar before you can start subtracting or adding their respective Chi-Squared distributions. You can show this by demonstrating that the covariance of Xi-Xbar (for i =1 to n) and just Xbar itself is zero. Once you've shown independence, you can easily reason with moment generating functions that the (n-1)S^2/sigma^2 term is in fact distributed as Chi-squared n-1.

[GladwinNewton]

Thanks man. Brilliant explanation. Finally found a mathematical proof with clarity. Thank you very much

[jitenkant]

Simply awesome.. loved the linearity of explanation

[sharonchetia]

So glad I came across this video. Cleared a lot of doubts I had

[mohssenify]

why books gives this as given finally i found the intuition behind it you re a life saver

[niketankotadiya]

hi professor can u tell me what chi-square statics says? if i say chi square of any distribution is 77.23. what does it mean

[mohssenify]

finally i found the proof i was looking for thank very much

[miodraglovric]

(1:33) standard deviation sigma squared?

[shuoyanpei]

Sir can you proof chi square goodness test too please.

[felipegomesdemelo]

Incredible and clear explanation!
Do you recomend any books for a complete statistics study?

[charlesAcmen]

still some flaws in the progress, proof should contain matrices to transform random variables