Question

- [10+10]A defective coin minting machine produces coins whose probability of heads is a continuous) random variable P with pdf f(p) = pep ,0<p<1 A coin produced by this machine is selected and tossed. a) Find the probability that the coin toss results in heads. ) Given that the coin toss resulted in heads, find the conditional pdf of P.

Answer 1

Solution @ probability that a coin toss result in heads green probability of heads with p.pt f (P) = pe, pt (1) Define the romdory valicable x as the first come of toos, result in heads P(X) = 1 f(x(p=P) & CPD de { pepel) de d'Prep de plow let uapr, de=elde - du = 2p dp irad p(x) = (pr 23. - s'apePap = (e) - 2 (pep- d' el do] (e) - 2 ( pel - ePh! = (e)-ale- e- Co-1)] = -2 e probability of coin tiss to heads = 6-2 By using Bayes teasery Splx (P) = f(x1p=P) Sp CD PLA)

PC Phan Heads) . PLA) pre pdf -2 = prep- ape P-208-2 e-2 fplx (053) = (053) 0.53 21053) e + 2 - 2 = 0.4772 - ?.foodt 3.3979-2 0.942 2 718-2 0.742 0.71828 = 0 . 1033 the conditional pot of peop = 0.1033