3. Let X and Y have the joint distribution as indicated in the following table: X=0 X=1 |Y=0 1/3 0 Y=1 0 1/3 Y=2 1/3 0 a. Give Y, the linear MMSE estimate for Y given X. b. Give the MSE for Ŷ₁. c. Give YM, the MMSE estimate for Y given X. d. Give the MSE for ÎM.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
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3. Let X and Y have the joint distribution as indicated in the following table:
X=0
X=1
Y=0
1/3
0
Y=1
0
1/3
Y=2
1/3
0
a. Give Ŷ, the linear MMSE estimate for Y given X.
b. Give the MSE for Ŷ₁.
c. Give YM, the MMSE estimate for Y given X.
d. Give the MSE for YM.
Transcribed Image Text:3. Let X and Y have the joint distribution as indicated in the following table: X=0 X=1 Y=0 1/3 0 Y=1 0 1/3 Y=2 1/3 0 a. Give Ŷ, the linear MMSE estimate for Y given X. b. Give the MSE for Ŷ₁. c. Give YM, the MMSE estimate for Y given X. d. Give the MSE for YM.
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