Mean square error
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 .