Math Problem Statement

If Cov(X,Y) = 4.4, then calculate Cov(1X,6Y)

Solution

To calculate the covariance Cov(1X,6Y)\text{Cov}(1X, 6Y), we can use the following property of covariance:

Cov(aX,bY)=abCov(X,Y)\text{Cov}(aX, bY) = ab \cdot \text{Cov}(X, Y)

Where aa and bb are constants.

In this case, a=1a = 1 and b=6b = 6. Thus,

Cov(1X,6Y)=1×6×Cov(X,Y)=6×4.4=26.4\text{Cov}(1X, 6Y) = 1 \times 6 \times \text{Cov}(X, Y) = 6 \times 4.4 = 26.4

So, Cov(1X,6Y)=26.4\text{Cov}(1X, 6Y) = 26.4.

Would you like more details on covariance or any other related topic?

Here are some related questions:

  1. What are other properties of covariance?
  2. How does covariance relate to correlation?
  3. What is the interpretation of positive and negative covariance?
  4. How can covariance be used in portfolio risk management?
  5. How does covariance apply to multiple variables?

Tip: Covariance measures the direction of a linear relationship between two variables but doesn't standardize their scales—correlation helps with that.

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Math Problem Analysis

Mathematical Concepts

Covariance

Formulas

Covariance formula: \( \text{Cov}(X, Y) = \mathbb{E}[(X - \mathbb{E}[X])(Y - \mathbb{E}[Y])] \)

Theorems

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Suitable Grade Level

Advanced Mathematics