A telemetry voltage V, transmitted from a position sensor on a ship's rudder, is a random variable with PDF:
fV(v)={1/32 0 −16<_v<_16, otherwise.
A receiver in the ship's control room receive R = V+X. The random variable X is a Gaussian (4,4) noise voltage that is independent of V. The receiver uses R to calculate a linear estimate of the telemetry voltage: V = aR+b.
(a) Find the expected value of the received voltage. E [R] = _______
(b) Find the variance of the received voltage. Var [R] = _________
(c) Find the covariance of the transmitted and received voltage. Cov [V, R] = _________
(d) Find the optimal linear estimate. VL (R) = __________
(e) Compute the minimum mean square error of the estimate. e* = __________
