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Assume that A and B are disjoint and that both events have positive .pdf

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Assume that A and B are disjoint and that both events have positive probability are they independent Solution Disjoint means they have no points in common. P( A intersection B) = 0 If A and B are independent, P(A intersection B) = P(A) P(B) So, this would imply P(A) P(B) =0 which would imply either P(A) or P(B) or both are zero while here both are positive The answer is \'no.\'.

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Assume that A and B are disjoint and that both events have positive probability are they independent Solution Disjoint means they have no points in common. P( A intersection B) = 0 If A and B are independent, P(A intersection B) = P(A) P(B) So, this would imply P(A) P(B) =0 which would imply either P(A) or P(B) or both are zero while here both are positive The answer is 'no.'

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  • 1. Assume that A and B are disjoint and that both events have positive probability are they independent Solution Disjoint means they have no points in common. P( A intersection B) = 0 If A and B are independent, P(A intersection B) = P(A) P(B) So, this would imply P(A) P(B) =0 which would imply either P(A) or P(B) or both are zero while here both are positive The answer is 'no.'