Let X be a uniform random variable in the interval (0,1). A coin is tossed twice and the results are denoted by Y1, Y2. Denote by 1 the outcome head and by 0 the outcome tail. We assume that the probability of heads is x and Y1, Y2 are independent if X is given. In particular, P(Y1=1,Y2=0∣X=x)=x(1−x),x∈(0,1). 

(i) Compute P(Y1=1,Y2=0) 

(ii) Compute the pdf of X given the event {Y1=1,Y2=0} .