Problem 3: LMS and LMS Let S denote the speed of a car on a particular segment of a highway, which is modeled as a Gaussian with mean 65 and variance 9. In this model, negative speeds are possible, however we ignore them since it is very unlikely. A policeman’s radar reading overestimates the speed by an amount N, where N is Gaussian with mean 0 and variance 1. Furthermore, it is known that S and N are jointly Gaussian with correlation coefficient 0.5. Find the LLMS estimator for a car’s speed as a function of radar reading.