If var(X)=50, var(X+Y)=80, and var(X-Y)=40, find var(Y) and cov(X, Y).

Name: Problem 43, Chapter 3: Statistics; Probability, Inference, and Decision
Uploaded: 2023-01-16T16:24:17-08:00
Duration: 1 min 47 s
Channel: Jacob Fry
Description: If var(X)=50, var(X+Y)=80, and var(X-Y)=40, find var(Y) and cov(X, Y).

step 1 In this question, we want to find an expression for the variance of x minus y. So the variance o

If var(X)=50, var(X+Y)=80, and var(X-Y)=40, find var(Y) and...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Linear Combinations of Random Variables

When dealing with the sum or difference of random variables, the variance of the resulting variable depends not only on the variances of the individual random variables but also on their covariance. Specifically, the formulas var(X+Y) = var(X) + var(Y) + 2cov(X, Y) and var(X-Y) = var(X) + var(Y) - 2cov(X, Y) are used to link these quantities and solve for unknowns.

Covariance

Covariance measures the degree to which two random variables change together. A positive covariance indicates that the variables tend to increase or decrease together, while a negative covariance suggests an inverse relationship. It is critical for understanding the linear relationship between variables.

Variance

Variance quantifies the variability or spread of a random variable around its mean. It is a fundamental concept in probability and statistics that helps in understanding the dispersion of data values and is used in various analyses, including risk assessment and hypothesis testing.

Transcript

Please give Ace some feedback