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 Xi be the value of pixel i . We observe, for each pixel the value of Yi = Xi + 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.

- Find E[Yi] . (Give a numerical answer.)
- Find