Consider 10 independent flips of a fair coin. These are two possible outcomes: O

Question

Consider 10 independent flips of a fair coin. These are two possible outcomes:
Outcome 1: HTHTHTHTHT
Outcome 2: HTHHTHTTHT

(a) Which of the two patterns above is more believable as an outcome?

(b) Compute the probability of each, is it consistent with your answer for part
(a) (it does not have to be)?

(c) Mr. Bayes to the rescue: consider the possibility that the coin flips are not
independent with P(T|H) = P(H|T) = p > 1=2, and that P(independent) =
P(dependent) = 1/2 (zero knowledge). Show how we can resolve the inconsistency
by using a Bayesian approach. Hint: compute P(independent outcome)
for each of the two outcomes. State a possible definition for believable in part (a).

Explanation / Answer

solution to part a) and b)
for the given two outcomes of 10 independent flips both outcomes are equally believable
this is so because both outcomes have equal probability of 1/210 =1/1024

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.