1. ( 45 pts) Suppose for the purposes of this rpastion that, for the 5 TL coins newly put into circulation, there has been a flar in mannfacturing. Suppoee it has been announced that 1/4 of these coins are biased; they have a probability p=1/4 of landing beads. The remaining 3/4 of the coins are fair: they have a probahility p=1/2 of landing beads. While shopping in a mall, a salesperson hands you a 5 TL coin for change, and you want to deternine if it is fair or biased. (a) (5 pis) Before doing any experiments with the coin, what is your decision? Is the enin fair or biased? What is the protahility of eare foe your derision? (b) ( 25 pts) Having learned Bayesinan decision thecry, you know that you can make a better dexision by making obervatioux; i.e, by simply tenoing the coin several times and looking at the outconeYou toss the coin n tisses, asd k out of these n tinos the coin lands heack. Show that the minimum probability of error decision rule as a finction of k and a is: Decide{biasedifk