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.

Quick! a survey of 57 customers was taken at a bookstore regarding the types of books purchased. the survey found that 33 customers purchased mysteries, 25 purchased science fiction, 18 purchased romance novels, 12 purchased mysteries and science fiction, 9 purchased mysteries and romance novels, 6 purchased science fiction and romance novels, and 2 purchased all three types of books. a) how many of the customers surveyed purchased only mysteries? b) how many purchased mysteries and science fiction, but not romance novels? c) how many purchased mysteries or science fiction? d) how many purchased mysteries or science fiction, but not romance novels? e) how many purchased exactly two types of books?

The radius of the earth is two times the radius of the moon. what fraction of the volume of the earth is the volume of the moon?

Determine the domain and range of the given function. the domain is all real numbers all real numbers greater than or equal to –2{x: x = –2, –1, 0, 1, 2}{y: y = –2, –1, 0, 1, 2}. the range is all real numbers all real numbers greater than or equal to –2{x: x = –2, –1, 0, 1, 2}{y: y = –2, –1, 0, 1, 2}.