What is an unbiased estimator? Proof sample mean is unbiased and why we divide by n-1 for sample var

In this video I discuss the basic idea behind unbiased estimators and provide the proof that the sample mean is an unbiased estimator. Also, I show a proof for a sample standard variance estimator that uses n in the denominator, and show that it is a biased estimator, therefore we use n-1 in the denominator to obtain an unbiased estimator for the population variance.

[parasraina]

I spent last 2 days trying to wrap around my head estimators and what it means to be unbiased. You explained me in minutes what I could not understand for days. I dont know how to thank you. You are the best. Thanks for the beautiful video

[nicholusmwangangi]

This stuff was giving me nightmares 😫 but you've simplified it in the best way possible. Thank you 🇰🇪

[faustinoeldelbarrio]

My mind is blown. Up until now all I had seen were simulations dividing by n Vs n-1, discussions on degrees of freedom etc. But this mathematical precise derivation is what I was looking for. THANK YOU.

[tatertot]

Wow. Incredible. The best proof of sample variance on YouTube. Thank you!

[SunilSandal-giyn]

Amazing! I was chasing to understand the meaning of biased and unbiased, but this video explains in a very simple way and with great explanation too. Thank you so much for the details.

[AlirezaSharifian]

It is a very good video that simply describes some jargon which usually is ignored in the literature.
Thank you.

[SSCthanos]

How amazingly you have explained this complicated thing is just beyond articulation ! Thank you so much

[anzirferdous]

You are the Best. You definitely deserve a ton more views and subscribers.

[derinncagan]

All of your videos are amazing!! As an Msc student I am checking out your videos for catch up and brushing up my informations. I am very happy to watch all of your videos they are clear and answering needs. Thanks!!

[fanfan]

Your channel is criminally underrated! Most videos on this topic will simply "proof" this empirically or talk about degrees of freedom without connecting it to anything. This is the first in dozens of videos I found that actually provides mathematical proof! Your explanation was excellent! I got to say at this point it's not super intuitive for me why it's -1 (and not any other number to make the Variance larger), but I can appreciate how the math supports it.

I just saw that you have tons of other videos on statistics and, if they are anything like this one, I know I will probably end up watching them and learning so much (=
Thank you for putting in so much time and energy! And for sharing your amazing Knowledge!

[catcen]

WOW! now we're taking! this is the best, literally the best! academic, clear, perfect! thank you so so much! maybe I put too many exclamation marks, but I mean it! THANKYOU THANKYOU THANKYOU

[noneofyourbusiness]

You are my personal hero for the month and probably the following months too cos I'm gonna start studying everything from your videos now

[Qwevo]

Am so happy I understood the concept. I found the finer details of the concept I was looking for.Thank you

[ycombinator]

I didn't know I will ever understand this... but here we are. Thanks!

Also, it gets called Bessel's correction. There should be a more rigorous proof out there but this is more then enough for me. Thank you!

[biaralier]

Thanks for breaking it down. and i mean the simple things like the meaning of an estimator. you the best ma'am.

[yassine]

I'm in a statistic / probability class this semester, which makes you, my new best friend 😁.
Thank you for the great explanation 👍👏

[momotaakter]

I was wasting hours and hours behind the topic, then I found your vedio❤

[sriramnb]

Beautiful. Amazing. I was waiting to see this kind of an explanation. Thanks

[charleslevine]

This was such a great video! Thank you!

[hwyum]

Thanks for clarification! One question here. Why var(X bar) equals to sigma^2 / n?