In essence a specific coin produced by this machine will have a fixed probability T=p of giving heads, but you do not know initially what that probability is. A coin produced by this machine is selected and tossed repeatedly, with successive tosses assumed independent.
a. Find the probability that the first coin toss results in heads.
b. Given that the first coin toss resulted in heads, find the conditional PDF of T.
c. Given that the first coin toss resulted in heads, find the conditional probability of heads on the second toss.