- #1

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if X= (3, 5, 7) & Y = (2, 4, 1)

What is the 3x3 covariance matrix for X & Y?

What is the 3x3 covariance matrix for X & Y?

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- #1

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if X= (3, 5, 7) & Y = (2, 4, 1)

What is the 3x3 covariance matrix for X & Y?

What is the 3x3 covariance matrix for X & Y?

- #2

mathman

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You have two variables, so the matrix is 2x2. The elements are var(X), var(Y) along the diagonal and cov(X,Y) off diagonal (both).if X= (3, 5, 7) & Y = (2, 4, 1)

What is the 3x3 covariance matrix for X & Y?

- #3

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Since 2x2 we need two diagonal elements and two off diagonal elements.

Are the following two elements**"off diagonal elements"**?

cov(X,Y) & cov(Y,X);

Are the following two elements

cov(X,Y) & cov(Y,X);

Last edited:

- #4

chiro

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Yes they are the off diagonal elements.

- #5

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The covariance between two jointly distributed real-valued **random variables** x and y with finite second moments is defined as-

1. cov(x,y)=E[(x-E[x])(y-E[y])]

The covariance between two jointly distributed real-valued**random vectors** x and y (**with m and n dimensional respectively**) with finite second moments is defined as

2. cov(x,y)=E[(x-E[x])(y-E[y])^{T}]

What is the difference between #1 & #2?

1. cov(x,y)=E[(x-E[x])(y-E[y])]

The covariance between two jointly distributed real-valued

2. cov(x,y)=E[(x-E[x])(y-E[y])

What is the difference between #1 & #2?

Last edited:

- #6

mathman

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In this context what do you mean by dimensional? X and Y are real valued. Do you mean the number of samples?The covariance between two jointly distributed real-valuedrandom variablesx and y with finite second moments is defined as-

1. cov(x,y)=E[(x-E[x])(y-E[y])]

The covariance between two jointly distributed real-valuedrandom vectorsx and y (with m and n dimensional respectively) with finite second moments is defined as

2. cov(x,y)=E[(x-E[x])(y-E[y])^{T}]

What is the difference between #1 & #2?

- #7

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Here is the link:In this context what do you mean by dimensional? X and Y are real valued. Do you mean the number of samples?

http://en.wikipedia.org/wiki/Covariance

- #8

mathman

Science Advisor

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1 refers to real valued (1 dimensional) random variables.random variablesx and y with finite second moments is defined as-

1. cov(x,y)=E[(x-E[x])(y-E[y])]

The covariance between two jointly distributed real-valuedrandom vectorsx and y (with m and n dimensional respectively) with finite second moments is defined as

2. cov(x,y)=E[(x-E[x])(y-E[y])^{T}]

What is the difference between #1 & #2?

2 is a generalization to vectors (n or m dimensional) which have random variables as components.

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