A defective coin minting machine produces coins whose probability of Heads is a random variable Q with PDF

Question

fQ(q)={5q4,0,if q∈[0,1],otherwise.


A coin produced by this machine is tossed repeatedly, with successive tosses assumed to be independent. Let A be the event that the first toss of this coin results in Heads, and let B be the event that the second toss of this coin results in Heads.

P(A)= 0.83333

(Your answer should be a number.)

Find the conditional PDF of Q given event A. Express your answer in terms of q using standard notation.

For 0≤q≤1, fQ∣A(q)=6⋅q5

P(B∣A)= 0.8571

(Your answer should be a number.)

Answer 1

Thanks, Friend. (Y)