c********y
发帖数: 2 | 1 Assume A1 and A2 are independent, are (B AND A1) and (B AND A2) also
independent? (no assumption on B whatsoever) Thanks! | r**********e
发帖数: 133 | 2 Not necessary, e.g., B intersects with both A1 and A2 but
B is disjoint with (A1 AND A2), then (B AND A1) AND (B AND A2)=0
which makes it impossible for the two events to be independent
as non-empty events need to intersect with each other to qualify
for independence. | g*******g
发帖数: 45 | 3
【在 r**********e 的大作中提到】
: Not necessary, e.g., B intersects with both A1 and A2 but
: B is disjoint with (A1 AND A2), then (B AND A1) AND (B AND A2)=0
: which makes it impossible for the two events to be independent
: as non-empty events need to intersect with each other to qualify
: for independence.
| b****t
发帖数: 22 | 4 not necessary.
for example, B=A1.
P((B&A1)&(B&A2))=P(A1&A2)
P(B&A1)=P(A1)
P(B&A2)=P(A1&A2)
if P(A1)<1 and P(A1&A2)>0, then
P(B&A1)P(B&A2)
【在 c********y 的大作中提到】
: Assume A1 and A2 are independent, are (B AND A1) and (B AND A2) also
: independent? (no assumption on B whatsoever) Thanks!
| e**c
发帖数: 195 | 5 I guess he was saying that B AND (A1 AND A2)=0.
E.g., A1={1,2},A2={1,3}, B={2,3}.
【在 g*******g 的大作中提到】
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