Suppose it is known that the probability of a head when a certain coin is tossed
ID: 3133896 • Letter: S
Question
Suppose it is known that the probability of a head when a certain coin is tossed is either 0.5 (coin #1) or 0.7 (coin #2). You must decide which value of p is correct. The loss from an incorrect decision is 1, and the loss from a correct decision is 0. The prior probabilities are P(p=0.5) = h_0 = 0.6, P(p=0.7) = h_a = 0.4.
A) What is your decision about the value of p after two tosses if you observed two heads?
B) If two heads were observed, for what values of h_0 should it be decided that coin #1 is the correct answer?
Explanation / Answer
a)
the decision about the value of p after 2 tosses if I observed 2 heads is 0.6
b)
h_0 will be for 2heads