Topic: Bayesian inference. Defective Coin.

1. Defective Coin A Bookmark this page Problem Set due Nov 9, 2022 12:59 CET Problem 1. Defective Coin 3 points possible (graded) A defective coin minting machine produces coins whose probability of Heads is a random variable @ with PDF fo (@) = [ 59*, if q e [0, 1], 10 , otherwise. A coin produced by this machine is tossed repeatedly, with successive tosses assumed to be independent. Let A be the event that the first toss of this coin results in Heads, and let _ be the event that the second toss of this coin results in Heads. 1. P (A) = ( Your answer should be a number.) 2. Find the conditional PDF of @ given event A. Express your answer in terms of q using standard notation. For 0