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 ?

Transcribed Image Text:

Pr(H, T) = 15, = 12 64 Pr(T, T) = 64 Pr(TH) = Pr(H,H) = 6 ,