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Repeat Exercise 2 12 if the probability assignment is changed to

Repeat Exercise 2.12 if the probability assignment is changed to:

An experiment consists of tossing a coin twice and observing the sequence of coin tosses. The sample space consists of four outcomes ξ1 = (H, H), ξ2 (H, T), ξ3 (T, H), and ξ4 (T, T). Suppose the coin is not evenly weighted such that we expect a heads to occur more often than tails and as a result, we assign the following probabilities to each of the four outcomes:

(a) Does this probability assignment satisfy the three axioms of probability?

(b) Given this probability assignment, what is ?

(c) Given this probability assignment, what is ?

An experiment consists of tossing a coin twice and observing the sequence of coin tosses. The sample space consists of four outcomes ξ1 = (H, H), ξ2 (H, T), ξ3 (T, H), and ξ4 (T, T). Suppose the coin is not evenly weighted such that we expect a heads to occur more often than tails and as a result, we assign the following probabilities to each of the four outcomes:

(a) Does this probability assignment satisfy the three axioms of probability?

(b) Given this probability assignment, what is ?

(c) Given this probability assignment, what is ?

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