Introduction to Probability & Statistics Expectations

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Presentation transcript:

Introduction to Probability & Statistics Expectations

Operational Rules Mutually Exclusive Events: P(A B) = P(A) + P(B) A

Conditional Probability Now suppose we know that event A has occurred. What is the probability of B given A? A A  B P(B|A) = P(A  B)/P(A)

Example Suppose for the same exponential distribution, we know the probability that the machine will last at least a more hrs given that it has already lasted c hrs. a c c+a Pr{X > a + c | X > c} = Pr{X > a + c  X > c} / Pr{X > c} = Pr{X > a + c} / Pr{X > c}    e c a  ( )