- #1

DUET

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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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- Thread starter DUET
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In summary, the 3x3 covariance matrix for X and Y would have two diagonal elements (var(X) and var(Y)), and two off diagonal elements (cov(X,Y) and cov(Y,X)). The difference between #1 and #2 is that #1 is for real valued random variables, while #2 is a generalization for vectors with random variables as components.

- #1

DUET

- 55

- 0

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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- #2

mathman

Science Advisor

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

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

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).

- #3

DUET

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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

DUET

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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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DUET said: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?

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

- #7

DUET

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Here is the link:mathman said: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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DUET said: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?

1 refers to real valued (1 dimensional) random variables.

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

A covariance matrix is a mathematical matrix that contains the variances and covariances between multiple variables. It is used to describe the linear relationship between two or more variables in a dataset.

A covariance matrix is calculated by taking the variance of each variable and the covariance between each pair of variables in a dataset. The resulting matrix will have the same number of rows and columns as the number of variables in the dataset.

A positive covariance in a covariance matrix indicates that the two variables have a positive linear relationship. This means that when one variable increases, the other variable also tends to increase.

A negative covariance in a covariance matrix indicates that the two variables have a negative linear relationship. This means that when one variable increases, the other variable tends to decrease.

The covariance matrix is important because it provides valuable information about the relationship between variables in a dataset. It is often used in statistical analysis and machine learning algorithms to understand the variability and dependencies between variables.

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