Proof that if events A and B are independent, so are Ac and B (and A and Bc)

Here I prove that if events A and B are independent, so are A complement and B. (And A and B complement, of course, since which event we call A and which we call B is arbitrary.)
Looking for a proof that if A and B are independent, so are their complements? That's here: • Proof that if two even...

[@tubesteaknyouri]

Thanks for your videos, especially the derivations and proofs. Those videos are helpful because there are not many resources that ease the transition from basic to advanced statistics. Moving to advanced statistics often feels like being slapped in the face with math.

[@amr3162]

This looks so simple i don't know why i got stuck on it. but i'm glad i checked my subscriptions instead of wasting another hour of my life. Thanks for the video!

[@jbstatistics]

You are welcome. For some reason, quite a few people have trouble with the first step in this one. The concept is pretty straightforward, but there's something about the formulas and symbols that can throw people off. And it's always easy to see once you know a correct path :)

[@christopherlindley8584]

Thank you so much, this was a massive help!!

[@resharamsawack1186]

Thank you! This was extremely helpful :)

[@flynngray8291]

Thanks, this is exactly what I was looking for

[@miguelmag]

Teacher thank you so much, great!!

[@Akasuki200]

Thanks a lot bro..!💖

[@user-yf1oy7fo3x]

Thank you!

[@AA-em3lw]

Thank you so much for this video! (:

[@jbstatistics]

Glad to be of help!

[@ashtonjohnson76]

So if the two events are independent, is there an overlap on a venn diagram? Is that the middle piece you discuss? Thanks.

[@tianchengxue5377]

This illustration looks nice and simple. But there is one question, you have to prove that P(B-A) = P(B) - P(A), for A, B being events of a probability space ( \omega, \italize F, P)?

[@yasinzamani9467]

Nice proof of a basic theorem : )
So based on that, we'll have these independencies:
A,B --> Ac,B --> B,Ac --> Ac,Bc

[@jbstatistics]

Yes. I agree that it's basic :) I've added it for completeness, and for the fact that I've often had students a little confused by this notion and I wanted to be able to point them to a video explanation.

[@mentesunidas8472]

HI, hope you are still here. Im just getting in to statistics. I just wanted to know how in the minute 3:17 you went from P(B) -p(A)*P(B) to P(B)(1-p(A))
You mention "factor that out", what does that means? thanks

[@jbstatistics]

What happens when you multiply P(B) through in P(B)(1-p(A))? You get P(B) - P(B)P(A). Factoring out P(B) is just working in the opposite direction; pulling out P(B) because it appears in both terms: P(B) - P(B)P(A) = P(B)(1-P(A)),.

[@farahsoliman8611]

ily

[@nighthardcore7808]

erm where is that other video you mention?????

[@jbstatistics]

The link's in the description: ruclips.net/video/bnDpZNlVZ3k/видео.html

[@dudeB15]

you are a god

[@chikeconcepta2245]

can you make video on moment generating function

[@jbstatistics]

Thanks for the suggestion. I get the moment generating function suggestion quite a bit. I may go that route soon, but I'm not sure at this point. I'll be doing a mix of basic probability (I do still teach intro stats quite often, and I need to fill in some of the blanks), some regression, and possibly some mathematical statistics. If I go the math stats route, I may very well do some on moment generating functions, as well as joint probability distributions.

[@chikeconcepta2245]

@@jbstatistics well good luck to the luck student who catches those videos in future when they can still be of aid, but honestly man the way you are able to explain this things in an easy to understand way ,you are a godsend bless you and your videos

[@jbstatistics]

@@chikeconcepta2245 Thanks for the kind words. I'm glad you've found my existing videos helpful!

[@beratakyar530]

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