W14 - Homework A

Due date: Tuesday 12/02, 11:59pm

Mean square error

01

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 .)

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02

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 .

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03

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 ?

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04

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 ?

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