A telemetry voltage V, transmitted from a position sensor on a ship's rudder, is a random variable with ![](https://test.transtutors.com/qimg/c728dc26-30b2-4191-a7eb-bfac74b2aa34.png)
A receiver in the ship's control room receives R = V +X, The random variable X is a Gaussian (0, √3) noise voltage that is independent of V. The receiver uses R to calculate a linear estimate of the telemetry voltage:
![](https://test.transtutors.com/qimg/b3c5b150-edf5-4e8c-91ab-d62f18ccc70d.png)
Find
(a) the expected received voltage E[R],
(b) the variance Var[R] of the received voltage,
(c) the covariance Cov[V, R] of the transmitted and received voltages,
(d) a∗ and b∗, the optimum coefficients in the linear estimate,
(e) e∗, the minimum mean square error of the estimate.