Statistics question (variance)

  • Context: Undergrad 
  • Thread starter Thread starter hanelliot
  • Start date Start date
  • Tags Tags
    Statistics Variance
Click For Summary
SUMMARY

The discussion centers on calculating the variance of the expression Var(X-2Y) given the variances of random variables X and Y, specifically Var(X) = 9 and Var(Y) = 1, along with the correlation p(X,Y) = 1/3. The correct formula for the variance of a linear combination of dependent variables is established as Var(X-2Y) = Var(X) + 4Var(Y) - 4Cov(X,Y). The covariance is computed using Cov(X,Y) = p(X,Y) * sqrt(Var(X) * Var(Y)).

PREREQUISITES
  • Understanding of variance and covariance in statistics
  • Familiarity with the properties of random variables
  • Knowledge of correlation coefficients and their implications
  • Ability to manipulate mathematical formulas involving variances
NEXT STEPS
  • Study the derivation of the variance formula for linear combinations of random variables
  • Learn how to compute covariance from correlation coefficients
  • Explore the implications of dependent versus independent random variables
  • Practice problems involving variance and covariance calculations
USEFUL FOR

This discussion is beneficial for students studying statistics, particularly those preparing for introductory courses in probability and statistics, as well as educators seeking to clarify concepts related to variance and covariance.

hanelliot
Messages
18
Reaction score
0
Studying for an intro course test and I have no one to compare it to right now.. any help would be appreciated.

Here is the question.

Q. Suppose X and Y are random variables such that p(X,Y)=1/3, Var(X) = 9 and Var(Y) = 1. Compute Var(X-2Y).

Since X and Y are not independent, we are using this formula: Var(X-Y) = Var(X) + Var(Y) - 2Cov(X,Y), correct?
So, Var(X-2Y) = Var(X) - 4Var(Y) - 2Cov(X,Y)? How do I proceed from here?
 
Physics news on Phys.org
hanelliot said:
Studying for an intro course test and I have no one to compare it to right now.. any help would be appreciated.

Here is the question.

Q. Suppose X and Y are random variables such that p(X,Y)=1/3, Var(X) = 9 and Var(Y) = 1. Compute Var(X-2Y).

Since X and Y are not independent, we are using this formula: Var(X-Y) = Var(X) + Var(Y) - 2Cov(X,Y), correct?
So, Var(X-2Y) = Var(X) - 4Var(Y) - 2Cov(X,Y)? How do I proceed from here?
First you have the get the correct equation:

Var(X-2Y) = Var(X) + 4Var(Y) - 4Cov(X,Y)
You have Var(X) and Var(Y) already.
I'll assume that p(X,Y) is the correlation function. If so Cov(X,Y)=p(X,Y)(Var(X)Var(Y))1/2.
 

Similar threads

Undergrad Conditional variance and total variance
  • · Replies 1 ·
Replies
1
Views
441
High School Variance & Standard Deviation
  • · Replies 42 ·
2
Replies
42
Views
6K
Undergrad An Alternative Variance Formula
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad What is the expected value of Cov(x,y)2 in an independent X and Y scenario?
  • · Replies 17 ·
Replies
17
Views
3K
MHB Find Cov(Z,W) with E(X^2)if X is N(0,1)
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Combining model uncertainties with analytical uncertainties
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Demonstration of inequality between 2 variance expressions
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Problem with calculating the cov matrix of X,Y
  • · Replies 24 ·
Replies
24
Views
3K
Undergrad How to calculate expectation and variance of kernel density estimator?
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Bivariate gaussians for ion beam optics
  • · Replies 7 ·
Replies
7
Views
3K