Question

A defective coin minting machine produces coins whose probability of heads is a random variable P with PDF peP, p [0,1], otherwise fp(p) A coin produced by this machine is selected and tossed repeatedly, with successive tosses assumed independent. (a) Find the probability that a coin toss results in heads. (b) Given that a coin toss resulted in heads, find the conditional PDF of P (c) Given that a first coin toss resulted in heads, find the conditional probability of heads on the next toss.

Answer 1

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Peld Then e-te-e-lo-) pote-2 Thesepse, probabitity that a win toss vesults in heads is ea b) Given that a co¡ท tossMeSultedm heads, find the Conditional POF OF P Given hat a com tos nSulted in heads,

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e-a e -& e- a Thesefore, the Condihonal poobabity of heads on the next toss given that he fist coin toss sulted in heads 18uy