a) It can be shown that the likelihood that the total emissions received by all detector pairs is y given that the expected number of emissions from all voxels is x is given by: P(y | x) = II i y; ! , where y, = E Cix, i (You don't have to show this. But for extra credits, you can do so using hints given at the end of this document.) Prove the final expression for the maximum likelihood estimation objective function fur- Hint: Take the logarithm of the likelihood and omit the constant term that does not depend on x