Factorization Theorem for Sufficient Statistics

Step by step, I work through the definition of sufficient statistic (intuitive vs formula, showing them equal) then interpreting the claim made in the factorization theorem, and then line by line, I give a proof of the discrete case in both directions.

[@existentialrap521]

Thx, Doc. We in the streets turning up to this one. Using exponential families right now for most sufficient statistic work, but I am hoping to get this theorem down well.
Also, you looking sharp, homie. I like the haircut and fit. Fresh.

[@pranavchandrav6071]

I'm studying to be an actuary, a big thanks to you for making these!

[@petrussd8881]

This is the most exact sufficiency video ever.

[@robertcruikshank4501]

Thank you very much! When I struggle to learn an idea, I try to spare others the same grief.

[@goosecouscous7658]

Watching this 30 mins before my final exam. Thank u 😭😭😭

[@williamkinum6941]

This video was incredibly helpful! Thank you for posting this.

[@aartikadu7282]

Your research behind the video, is crystally clear, making very easy to understand.
Kindly we want more statistical videos. 😄

[@yifuli9390]

Hey, great stuff. Please keep up the good work. Much love!

[@denisegandara7290]

Great explanation! Thank you!

[@TheSGOGS]

thank you mr cruikshank

[@kctsou821118]

This video helps a lot, thanks

[@robertcruikshank4501]

Glad to hear it!

[@DarioGreco21]

Thank you !

[@timothykelebeng5230]

brilliant

[@4th_wall511]

I love you.

[@Dupamine]

Man you are confusing as hell

[@robertcruikshank4501]

Sorry the video didn't work for you. It IS a confusing topic. Where did you get lost? The first couple of minutes explain the definition of sufficient, and I cover that separately in at least one other video.
What do you think would help? Some examples?

[@Dupamine]

@@robertcruikshank4501 I will try to explain where I got confused at 1:09 you explain P(theta|x)=p(theta) is definiton of independence. I understand that.
After that you say 'that means' and write some equation after that. How does that mean the next equation( P(theta and X= p(theta).p(X))?

[@Dupamine]

@@robertcruikshank4501 hay man u just dissapeared everything fine with wife and family?

[@robertcruikshank4501]

@@Dupamine Sorry I missed this until just now. There are three equivalent definitions of independence. Remember the definition of conditional probability P(A|B) = P(A and B)/P(B), so saying P(A|B) = P(A) is the same thing as saying P(A) = P(A and B)/P(B) or P(A) P(B) = P(A and B).

[@Dupamine]

@@robertcruikshank4501 thanks man