3. 15 pt A defective coin minting machine produces coins whose probability of heads is a random variable P with PDF pep. p 6 [0,1], 0, otherwise. fP(P) = { A coin produced by this machine is selected and tossed repeatedly, with successive tosses assumed independent. (a) 5 pt Find the probability that a coin toss results in heads. (b) 5 pt Given that a coin toss resulted in heads, nd the conditional PDF of P. (c) 5 pt Given that a rst coin toss resulted in heads, nd the conditional probability of heads on the next toss