3. A defective coin minting machine produces coins whose probability of heads is

Question

3. A defective coin minting machine produces coins whose probability of heads is a random variable P with PDF p E [0, 1 fr(p)-> pe", 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 a first coin toss resulted in heads, find the conditional probability of heads on the next toss.

Explanation / Answer

A) probabiloty of head is p which ranges from[0,1] as p is the randomvariable of probability of head.

b) P( probability of head/ already a head occured)= P( probability of head / p=1) = e

c) as the two tosses are independent so probability of head will be indepemdent of the previous toss ans hence probability= pe^p

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