1. Given Poisson distribution with parameter 1: (AT) PT(X = k) = k! exp(-XT), (1) (a) Find the variance of the distribution. (b) Go back to Problem 3 of Homework 8. For each quadrant of the checker object and for each illumination factor, estimate the SNR as: nominal quadrant value SNR(dB) = 20 log10 standard deviation of error (2) where the error for each pixel is the difference between the nominal and the actual values. Plot the SNR as a function of the illumination factor. Although not required, you may want to consider using a log or semiog scale for the plots. Provide some explanation of the logic you used for the computation rather than just providing the code. 2. Consider the detector in Problem 1 of the supplemental problem set provided to you on blackboard. Assuming shot noise is the dominant noise and the measurement bandwidth is 500 MHz, evaluate the NEP and the detectivity. 1. Given Poisson distribution with parameter 1: (AT) PT(X = k) = k! exp(-XT), (1) (a) Find the variance of the distribution. (b) Go back to Problem 3 of Homework 8. For each quadrant of the checker object and for each illumination factor, estimate the SNR as: nominal quadrant value SNR(dB) = 20 log10 standard deviation of error (2) where the error for each pixel is the difference between the nominal and the actual values. Plot the SNR as a function of the illumination factor. Although not required, you may want to consider using a log or semiog scale for the plots. Provide some explanation of the logic you used for the computation rather than just providing the code. 2. Consider the detector in Problem 1 of the supplemental problem set provided to you on blackboard. Assuming shot noise is the dominant noise and the measurement bandwidth is 500 MHz, evaluate the NEP and the detectivity