(a) Let X be a random variable with finite variance. Let Y = ax + 3 for some numbers a, ß E R. Compute 1₁ = E[(Y - E[Y|X])²]. (b) Again, let X be a random variable with finite variance. Additionally, let A ~ U(-1, 1) such that X and A are independent and consider Y = AX. You may use without proof that A² 1 X². Compute 12 = E[(Y - E[YIX])2] expressing your final result in terms of E[X] for some value or values of k that you should specify. (c) [TYPE:] Provide an interpretation of the quantities ₁ and 2 obtained in parts (a) and (b) above in terms of the ability to predict Y given the value of X and explain any difference you observe.
(a) Let X be a random variable with finite variance. Let Y = ax + 3 for some numbers a, ß E R. Compute 1₁ = E[(Y - E[Y|X])²]. (b) Again, let X be a random variable with finite variance. Additionally, let A ~ U(-1, 1) such that X and A are independent and consider Y = AX. You may use without proof that A² 1 X². Compute 12 = E[(Y - E[YIX])2] expressing your final result in terms of E[X] for some value or values of k that you should specify. (c) [TYPE:] Provide an interpretation of the quantities ₁ and 2 obtained in parts (a) and (b) above in terms of the ability to predict Y given the value of X and explain any difference you observe.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![(a) Let X be a random variable with finite variance. LetY = aX + B for some
numbers a, B e R. Compute l1 = E[(Y – E[Y|X])²].
(b) Again, let X be a random variable with finite variance. Additionally, let A ~
U(-1,1) such that X and A are independent and consider Y = AX. You may
use without proof that A? 1 X². Compute l2 = E [(Y – E[Y|X])²] expressing
your final result in terms of EX*] for some value or values of k that you should
specify.
(c) [TYPE:] Provide an interpretation of the quantities lį and l2 obtained in parts
(a) and (b) above in terms of the ability to predict Y given the value of X and
explain any difference you observe.
!!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e20d631-fe19-4520-8c4c-3300def40bfb%2Fa98dd329-9e4e-4245-b722-00bda1d6af90%2Fs8is66b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Let X be a random variable with finite variance. LetY = aX + B for some
numbers a, B e R. Compute l1 = E[(Y – E[Y|X])²].
(b) Again, let X be a random variable with finite variance. Additionally, let A ~
U(-1,1) such that X and A are independent and consider Y = AX. You may
use without proof that A? 1 X². Compute l2 = E [(Y – E[Y|X])²] expressing
your final result in terms of EX*] for some value or values of k that you should
specify.
(c) [TYPE:] Provide an interpretation of the quantities lį and l2 obtained in parts
(a) and (b) above in terms of the ability to predict Y given the value of X and
explain any difference you observe.
!!
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