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 .