A defective coin minting machine produces coins whose

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QUESTION:

A defective coin minting machine produces coins whose probability of heads is a random variable P with PDF jp (p) = { peP , p E [O, ], 0, otherwise. 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 the first coin toss resulted in heads, find the conditional probability of heads on the next toss.

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QUESTION:

A defective coin minting machine produces coins whose probability of heads is a random variable P with PDF jp (p) = { peP , p E [O, ], 0, otherwise. 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 the first coin toss resulted in heads, find the conditional probability of heads on the next toss.

ANSWER:

Step 1 of 4

(a)To find: Probability that a coin toss results in heads

Given: Probability of heads with

Define the random variable  as the first coin toss resulted in heads.

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