I need help with my statistic and probability question.

[30 pts] 5. A coin minting machine produces coins whose probability of heads is a random variable P with PDF fp (p) = Ce (p-0.5)2 2 if O Sps1. 0 otherwise A coin produced by this machine is selected and tossed repeatedly, with successive tosses assumed independent. (a) Determine the value of the constant C. [5 pts] (b) Find the probability that a coin toss results in heads. [7 pts] (c) Given that a coin toss resulted in heads, find the conditional PDF of P. [8 pts] (d) Given that the first coin toss resulted in heads, find the conditional probability of heads on the next toss. [10 pts]