Practice Problems on Covariance Matrix
Problem 1: Given two sets of data points: X = [2, 4, 6, 8, 10] and Y = [1, 3, 5, 7, 9], calculate the covariance between X and Y.
Problem 2: Calculate the covariance matrix for the following dataset:
X1 | X2 | X3 |
|---|---|---|
4 | 2 | 0 |
4 | 5 | 6 |
8 | 10 | 12 |
12` | 9 | 6 |
Problem 3: Given the covariance matrix:
[Tex]\Sigma = \begin{bmatrix} 4 & -2 & 0 \\ -2 & 3 & 1 \\ 0 & 1 & 5 \\ \end{bmatrix}[/Tex]
Identify the variances and covariances between the variables.
Covariance Matrix
Covariance Matrix is a type of matrix used to describe the covariance values between two items in a random vector. It is also known as the variance-covariance matrix because the variance of each element is represented along the matrix’s major diagonal and the covariance is represented among the non-diagonal elements.
It’s particularly important in fields like data science, machine learning, and finance, where understanding relationships between multiple variables is crucial and comes in handy when it comes to stochastic modeling and principal component analysis.
In this article, we will discuss about various things related to Covariance Matrix such as it’s definition, example, and formula as well.
Table of Content
- What is Covariance Matrix?
- Covariance Matrix Example
- Covariance Matrix Formula
- 2 ⨯ 2 Covariance Matrix
- 3 ⨯ 3 Covariance Matrix
- How to Find Covariance Matrix?
- Properties of Covariance Matrix
- Solved Examples
- Practice Problems
- FAQs
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