Suppose you have a joint distribution of x and y where • x has population mean lg and population variance o • y has population mean ly and population variance o and the population covariance between them is Ery. The population Pearson correlation is then given by Ery We collect n pairs of data, (xi, Yi), i = 1, .., n. Each pair is an independent draw from this distribution. (a) Suppose we estimate our population covariance with n 1 E(t; – Ha)(yi – Hy). i=1 Is this an unbiased estimator of the population covariance? Show why or why not.
Suppose you have a joint distribution of x and y where • x has population mean lg and population variance o • y has population mean ly and population variance o and the population covariance between them is Ery. The population Pearson correlation is then given by Ery We collect n pairs of data, (xi, Yi), i = 1, .., n. Each pair is an independent draw from this distribution. (a) Suppose we estimate our population covariance with n 1 E(t; – Ha)(yi – Hy). i=1 Is this an unbiased estimator of the population covariance? Show why or why not.
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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Transcribed Image Text:Suppose you have a joint distribution of x and y where
• x has population mean ug and population variance o?
• y has population mean ly and population variance o,
and the population covariance between them is Ery. The population Pearson correlation is
then given by
Ery
OxJy
We collect n pairs of data, (X;, Yi), i = 1,.. , n. Each pair is an independent draw from this
distribution.
(a)
Suppose we estimate our population covariance with
n
1
(x; – Ha)(yi – µy).
i=1
Is this an unbiased estimator of the population covariance? Show why or why not.
(b)
Suppose we estimate our correlation with
(xi – Ha)(Yi – Hy)
-
n
i=1
Ox0y
Is this an unbiased estimator of the population correlation? Show why or why not.
=WI
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