3. Assume that we have a CCD camera system that is cooled so that noise due to dark current is negligible. Then digitized pixel values will be given by D=(S+NA+NP)A+NQ where S is the signal in electrons, NA is the zero-mean amplifier noise source with variance A2, NP is the zero-mean photon noise with variance S,A is the gain of the amplifier, and NQ is the zero-mean quantization noise with variance Q2. Assume that the noise sources are independent. a) Show that for a constant signal level S the expected value of D is =SA and the variance of D is given by D2=A+C2 where C2=A2A2+Q2