Consider an image, in which every pixel takes a value of 1, with probabilities q, and a value 0

Consider an image, in which every pixel takes a value of 1, with probability q, and a value 0, with probability 1 q, where q is the realized value of a random variable Q which is distributed uniformly over the interval [0, 1]. The realized value q is the same for every pixel. Let X,- be the value of pixel i. We observe, for each pixel the value of Y,- = X, + N, where N is normal with mean 2 and unit variance. (Note that we have the same noise at each pixel.) Assume that, conditional on Q, the Xi's are independent, and that the noise N is independent of Q and the Xi's. 1. Find E[Y,]. (Give a numerical answer.) Ell/2] = 2. Find Var[Y;]. (Give a numerical answer.) Var[Y,-] = 3. Let A be the event that the actual values X1 and X2 of pixels 1 and 2, respectively, are zero. Find the conditional probability of Q given A. (Enter your answer in terms of q in standard notation.) ForOSqSl: fQ|A(I) =