Let E, E2,... be a partition of the sample space 2. Given an event A, define...

  

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Let E₁, E2,... be a partition of the sample space 2. Given an event A, define the sets A₂: An E₂. you know that the sets A, fo partition of A. Using this, prove the partition theorem. That is, show that P(A) = ΣP(A[E;)P(E.) . (You may assume that P(E;) > 0 for all E..) Let E₁, E2,... be a partition of the sample space 2. Given an event A, define the sets A₂: An E₂. you know that the sets A, fo partition of A. Using this, prove the partition theorem. That is, show that P(A) = ΣP(A[E;)P(E.) . (You may assume that P(E;) > 0 for all E..)

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ANSWER To prove the partition theorem we start with the definition of conditional probability PA E PAE PE where PA E is the probability of A given tha... View the full answer