Question

An image , corrupted with noise, has pixels which take the value 1 with probability q and 0 with probability 1−q, with q being the value of a random variable Q which is uniformly on [0,1]. Xi is the value of pixel i, but we observe Yi=Xi+N for each pixel. N is normal and has mean =2 and unit variance. The q and N is the same for every pixel, and conditioned on Q, every Xi is independent. The noise is independent of Q and every Xi. Let A be the event that the actual values of X1 and X2, (the first and second pixels) are =0.

find:E[Yi], Var[Yi] and fQ|A(q) (conditional probability of Q given A, as a function of q) for 0≤q≤1

My working so far:
E[Xi] = bernoulli RV, so E[Xi] = q = 0.5 (Q is uniform on [0,1])
E[Yi] = E[Xi] + E[N]
= q + 2 = 2.5
Var[Yi] =Var[Xi] +Var[N]
= q(1-q) + 1
= 0.5*0.5 + 1 = 1.25
P(X1 = 0) = 1-q = P(X2 = 0)
fQ(q) = 1 (uniform on [1,0])
fA(q) = ? =
fQ|A(q) = (fQ(q) * fA|Q(q)) / fA(q) ?
fQ|A(q) = (1*(1-q)*(1-q))/?)