Proof that the Sample Variance is an Unbiased Estimator of the Population Variance

One of the best explanations for why n-1 is used for sample variance. Thank you so much!

Great❤

Thank you sir

Why do we not use |Xi - x̄ | instead of (Xi - x̄ )² ?

my lecturer did this in 5 steps in the lecture notes, thanks for actually teaching me it

This video was a life saver.

great explanation sir!

Great video! I have a question though-- Why are we taking the expected value of the equation?

so here x is beta, and x bar is beta hat , corresponding , as in Gauss MArkov theorem?

Sending you lots of hugs, this saved me ❤❤❤❤😭😭

great explanation for ordinary humans ;-)😇

what the hell

Where can i find the proof for these two relationships at the beginning where
E(summation Xi) = summation E(Xi)?
E(eX) = eE(X)

All of your videos are amazing. They are very helpful with my mathematics class. I am grateful for your help!

beautifully done! thanks!

I covered this proof when I was back at school, and I was looking for a reference to refresh my memory. I spent over an hour googling trying to remember the details of the proof, but all pages I ran into are ambiguous with no clear/consistent notations

this 6 minutes videos are concise and clear, and saved me spending more time!

Thank you!

Is X bar same as mean mu here?

THX!!!!!!!!!

Awesome video! Thank you!

Cleanest, simplest and most importantly, rigorous proof why we divide by (n-1) and not n. Thank you for this video!

Nnnnnnnnice !

Wow wow wow....
Now I got rid of this thorny term (n-1) in the denominator 😃

That was magic! An unbiased estimator🤯

Suprb job 👍🤗

I am taking my first econometrics course, and my professor just did a review of prob & stats. He did not take the time to go through the steps, so I was beginning to feel anxious about moving foward. This video helped me better understand the concepts he just went over. Thank you!

Thanks for this video. Such a complicated topic is explained in such an easy manner. Hats off to you🙇‍♂️

thannnnnnnnnnk you so much 😭😭😭

Every step of the logic is crystal clear, BUT I CAN'T INTUITIVELY SEE WHY?!

I’m glad I found this video

Clear as daylight. Thank you sir.

such a good video....... thanks for helping me clean an important concept!!!!

Could anyone explain to me shortly why variance of each X_i is equal to \sigma^2? Thank you in advance :)

Best Explanation Yet!! Thanks!

how did u derive eqns for E( x^2) and E(xbar^2) ??

Excellent!

Awsome video!

Thank you so much maaaan!

Thanks a lot from korea

Thank you

Thank you God bless you

thank you king

Finally!!! A proof versus explaining, “Obviously then, you divide by the Degrees of Freedom.”

sometimes hand-wavy explanations don't really convince me. Thanks for this