A defective coin minting machine produces coins whose probability of heads is a random variable Q with PDF fQ(q) = qeq; q 2 [0; 1]; 0; otherwise In essence, a speci c coin produced by this machine will have a xed probability Q = q 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) Given that there were exactly two heads in the rst three coin tosses, nd the con- ditional probability of heads on the fourth toss. (b) Given that there were exactly two heads in the rst three coin tosses, nd the con- ditional probability that the rst toss was heads.