Problem 1. [SW 14.6] In Exercise 14.5(b) (which is copied below for your reference), suppose you predict Y using Y/2 instead of Y. Hint: Notice that in this exercise, Y is an out-of-sample value with respect to the sample we have. In other words, Y is not part of the sample, so it does not enter the formula for Y = // (Y₁ + Y₂ + ... + Y₁0). (g) In a realistic setting, the value of u is unknown. What advice would you give someone who is deciding between using Y and Y/2? For reference, here is Exercise 14.5(b). (It is not part of this problem set, but it may be helpful for you to do this exercise before attempting 14.6.) Y is a random variable with mean μ = 2 and variance o² = 25. Suppose you don't know the value of u but you have access to a random sample of size n = 10 from the same population. Let Y denote the sample mean from this random sample. You predict the value of Y using Y.
Problem 1. [SW 14.6] In Exercise 14.5(b) (which is copied below for your reference), suppose you predict Y using Y/2 instead of Y. Hint: Notice that in this exercise, Y is an out-of-sample value with respect to the sample we have. In other words, Y is not part of the sample, so it does not enter the formula for Y = // (Y₁ + Y₂ + ... + Y₁0). (g) In a realistic setting, the value of u is unknown. What advice would you give someone who is deciding between using Y and Y/2? For reference, here is Exercise 14.5(b). (It is not part of this problem set, but it may be helpful for you to do this exercise before attempting 14.6.) Y is a random variable with mean μ = 2 and variance o² = 25. Suppose you don't know the value of u but you have access to a random sample of size n = 10 from the same population. Let Y denote the sample mean from this random sample. You predict the value of Y using Y.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![Problem 1. [SW 14.6] In Exercise 14.5(b) (which is copied below for your reference), suppose you
predict Y using Y/2 instead of Y. Hint: Notice that in this exercise, Y is an out-of-sample value
with respect to the sample we have. In other words, Y is not part of the sample, so it does not enter
the formula for Y = 1/2 (Y₁ + Y₂ + ... + Y10).
n
(g) In a realistic setting, the value of µ is unknown. What advice would you give someone who is
deciding between using Y and Y/2?
For reference, here is Exercise 14.5(b). (It is not part of this problem set, but it may be helpful
for you to do this exercise before attempting 14.6.) Y is a random variable with mean = 2 and
variance o² = 25. Suppose you don't know the value of μ but you have access to a random sample
of size n = 10 from the same population. Let Y denote the sample mean from this random sample.
You predict the value of Y using Y.
(i) Show that the prediction error can be decomposed as Y -Y = (Y – µ) – (Ỹ – µ), where Y - μ
is the prediction error of the oracle predictor and fl Y is the error associated with using Y
as an estimate of μ.
(ii) Show that (Y-μ) has a mean of 0, that (Y− µ) has a mean of 0,
and that Y - Y has a mean of 0.
(iii) Show that Y - μ and Y - μ are uncorrelated.
(iv) Show that the MSPE of Y is MSPE = E (Y − µ)² + E (Ỹ − µ)² =
(v) Show that MSPE = 25 (1 + 1) = 27.5.
= var (Y) + var (Y).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61ff295b-afd4-43c3-8ed2-2cc17b9c2249%2Fc1730fa6-3eab-4f9c-ab24-d1a5a2cfd49b%2Facq0gij_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 1. [SW 14.6] In Exercise 14.5(b) (which is copied below for your reference), suppose you
predict Y using Y/2 instead of Y. Hint: Notice that in this exercise, Y is an out-of-sample value
with respect to the sample we have. In other words, Y is not part of the sample, so it does not enter
the formula for Y = 1/2 (Y₁ + Y₂ + ... + Y10).
n
(g) In a realistic setting, the value of µ is unknown. What advice would you give someone who is
deciding between using Y and Y/2?
For reference, here is Exercise 14.5(b). (It is not part of this problem set, but it may be helpful
for you to do this exercise before attempting 14.6.) Y is a random variable with mean = 2 and
variance o² = 25. Suppose you don't know the value of μ but you have access to a random sample
of size n = 10 from the same population. Let Y denote the sample mean from this random sample.
You predict the value of Y using Y.
(i) Show that the prediction error can be decomposed as Y -Y = (Y – µ) – (Ỹ – µ), where Y - μ
is the prediction error of the oracle predictor and fl Y is the error associated with using Y
as an estimate of μ.
(ii) Show that (Y-μ) has a mean of 0, that (Y− µ) has a mean of 0,
and that Y - Y has a mean of 0.
(iii) Show that Y - μ and Y - μ are uncorrelated.
(iv) Show that the MSPE of Y is MSPE = E (Y − µ)² + E (Ỹ − µ)² =
(v) Show that MSPE = 25 (1 + 1) = 27.5.
= var (Y) + var (Y).
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