Be Careful! There's a big mistake in this video. (One of) The definition(s) of random variables A and B being independent is: P(A , B) = P(A) * P (B) and not what's written on the right hand side (i.e. using the conditional probability, P(B|A)...) . The mistake is caused because on the left hand side it should have been P(B, A)/P(A) = P(B)/1 . The reason for it is that P(B|A) , i.e. the probability that B occurs, when we know A occurred, is equal to P(A,B) (=the probability both occurred) divided by P(A) - the probability A occurred (this is the *definition* of conditional probability). The teacher here accidentally replaced the joint probability with the conditional without noticing.
Be Careful! There's a big mistake in this video. (One of) The definition(s) of random variables A and B being independent is: P(A , B) = P(A) * P (B) and not what's written on the right hand side (i.e. using the conditional probability, P(B|A)...) . The mistake is caused because on the left hand side it should have been P(B, A)/P(A) = P(B)/1 . The reason for it is that P(B|A) , i.e. the probability that B occurs, when we know A occurred, is equal to P(A,B) (=the probability both occurred) divided by P(A) - the probability A occurred (this is the *definition* of conditional probability). The teacher here accidentally replaced the joint probability with the conditional without noticing.
Thanks for the warning! I'll go and look somewhere else for a full of understanding of independence.
This is why we need the dislike button back
So independence is not necessarily categorical. I wonder if there is a continuous measure of how independent two events are.