Consider an experiment corresponding to the single throw of a die. Let E ₁ be the event that throw is one of {1, 2, 3, 4} and let E ₂ the event that throw is one of {3, 4, 5, 6}. You are given that P(E ₁ ) = P(E ₂ ) = 2/3.

(a) Identify the smallest σ-algebra A sat containing the events E ₁ and E ₂ .

(b) Attach probabilities P(J) to all the elements J ∈ A.

(c) What can you say about the probability P({1}) of the event associated to a throw of 1 ? Be as precise as you can be.

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a Let A smallest algebra A 1 2 3 4 3 4 5 6 1 2 5 6 1 2 5 6 3 4 Check ... View the full answer