The Rao-Blackwell Theorem Explained

[@amina0218]

Please, don't stop creating the content! I am so grateful for you! The stats at universities are not properly explained, infortunately, you make difficult things seem easy indeed!

[@statswithbrian]

Thank you, much more to come! :)

[@RoyalYoutube_PRO]

Thanks a lot for making this... Very very helpful

[@jakeaustria5445]

Thank You

[@andrashorvath2411]

Great video, only let me express to you that you jumped a huge step when introducing the Poisson equation into the one that simplifies to ((n-1)/n)^t. Why did you transform the probability formalization into that equation? A huge step and I think many might lost the track here. It would be nice if you added the explanation in a comment. Thanks.

[@statswithbrian]

The data follows a Poisson distribution, so anything would need to be eventually translated into something involving the Poisson formula. It relies on the fact that X1 follows a Poisson (lambda) distribution, sum of x2…xn follows a Poisson ((n-1)lambda) distribution, sum of x1…xn follows a Poisson (n*lambda) distribution

[@carl3260]

Hi Brian, nice explanation. I was wondering what a more formal approach to deriving the expression at 13:00 might look like? The intuitive "approach" mentioned, which makes sense, implicitly sums over a (latent) variable indicating which X_i is maximal. But I'm not sure how else you could go about it, e.g. the earlier method calculated p(X_1, max(X_i) = t) / p(max(X_i) = t), but that doesn't seem available, e.g. how is p(max(X_i) = t) defined? Many thanks!

[@statswithbrian]

You're right that a similar method as before doesn't seem available to us, because we can't easily separate the maximum in the same way as we can the rest of the sum/mean in the Poisson example. I think one could show a little more work in the example, but I can't think of a method that wouldn't at least require using the law of total probability/expectation in the same way, where we add in the conditioning on whether or not X1 is also the max.

[@kelvinwannnn7594]

You made a great explanation better than my professor! Can you make a Video about completeness statistics ?

[@statswithbrian]

I'm thinking about it - someone requested a minimal sufficient statistic video today, so I might create a playlist with a short video on completeness.