A defective coin minting machine produces coins whose probability of Heads is a random variable Q with PDF
fQ(q)={5*q^4 if q∈[0,1]
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)=?
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)=?
P(B∣A)=