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class03_4 - 1.017/1.010 Class 4 Joint Probability,...

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1.017/1.010 Class 4 Joint Probability, Independence, Repeated Trials Joint Probabilities and Independence Joint probability of 2 events A and B defined in the same sample space (probability that outcome lies in A and B ): P ( AB ) = P ( C ) ; where event C = A B= AB I If A and B are independent then: P ( AB ) = P ( A ) P ( B ) Note that mutually exclusive events are not independent since if one occurs we know the other has not. Example: Consider the following events A and B defined from a die toss experiment with outcomes { 1, 2, 3, 4, 5, 6 } A = {2, 4 ,6} B = {1, 2 ,3, 4} Then: P ( A ) = 1/2 , P ( B ) = 2/3, P( AB ) = 2/6 = P ( A ) P ( B ) So A and B are independent. Composite experiments Related experiments are often conducted in a sequence. For example, suppose we toss a fair coin (with 2 equally likely outcomes { H T }) and then throw a fair die (with 6 equally likely outcomes { 1, 2, 3, 4, 5, 6 }). This process can be viewed as two separate experiments E 1 and E 2 with different sample spaces. Or … it can be viewed as a single composite experiment
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class03_4 - 1.017/1.010 Class 4 Joint Probability,...

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