Question 4 (5 points A sensor needs to be characterized under lab conditions . Let the lab ideal measured values be denoted by a [n], n = 0, 1,..., N, then the sensor ponze is described by the following equation I [n] = (8 [n] + a t w[n] n = 0, 1, . .., N, (1) where r n] is the sensor measurement , is the unknown sensor parameter and w is the noise on the system that is uncorrelated (uncorrelated Over time and uncorrelated with an) with w ~ N(0, g?) Vn 0.5. State the binary hypothesis for detecting sensor failure versus functionality. (2 pts ) (c) Derive the likelihood ratio test (LRT ) for detecting the sensor functionality and determine the Neyman-Pearson detector T (x) and threshold