- #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?
DUET said:if X= (3, 5, 7) & Y = (2, 4, 1)
What is the 3x3 covariance matrix for X & Y?
DUET said: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?
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?
DUET said: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?
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.