01
MSE of a derived variable
Suppose that
, and . You are using the sample mean with 50 samples, namely
, to estimate . What is the mean square error of
? (Errors are deviations of this variable from .)
02
Estimates from joint PDF
Suppose
and have the following joint PDF: (a) Find
and the blind estimate . (b) Compute
, the MMSE estimate of assuming the event . (c) Find
and the blind estimate . (d) Compute
, the MMSE estimate of assuming the event .
03
MMSE exact estimator from joint PDF
Suppose
and have the following joint PDF: (a) What is
, the MMSE estimate of given ? (b) What is
, the MMSE estimate of given ?
04
MMSE linear estimator from joint PDF
Suppose
and have the following joint PDF: (a) What is
, the MMSE linear estimator of in terms of ? (b) What is
, the MMSE linear estimator of in terms of ?
05
MMSE linear estimator from joint PMF
Suppose
and have the following joint PMF:
0 0 (a) Find the minimal MSE linear estimator for
in terms of . (b) What is the MMSE error for this linear estimator?
(c) Use (a) to estimate
given and .
06
MMSE linear estimator from joint density
Consider this joint PDF:
(a) What is the minimal MSE linear estimator for
in terms of ? (b) What is the linear estimate of
given ? (You may use the data you found in W09-B Q8, you don’t need to repeat those calculations.)
07
Telemetry signal
A telemetry signal,
, transmitted from a temperature sensor on a communications satellite is a Gaussian random variable with and . The receiver at mission control receives , where is a noise voltage independent of with PDF: The receiver uses
to calculate a linear estimate of the telemetry voltage: (a) What is
, the expected value of the received voltage? (b) What is
, the variance of the received voltage? (c) What is
, the covariance of the transmitted voltage and the received voltage? (d) What is the correlation coefficient
of and ? (e) What are
and , the optimum mean square values of and in the linear estimator? (f) What is
, the minimum mean square error of the linear estimate?