Problem 6. [16 points]. Consider a signal detector with an input r = ±A+n where +A and -A occur with equal probability and the noise variance n is characterized by the Laplacian density p(n) = 1 e-In√2/0 a. Derive the probability of error as a function of A and σ. b. Find the SNR (= A2/02) required to achieve an error probability of 10-5. c. Repeat part (a) for the Gaussian density 1 p(n): -n²/202 = 2πσ d. Repeat part (b) for the above Gaussian density and compare the results you got using the Laplacian and Gaussian densities.