Asked by Kayla Preston on Sep 26, 2024
Verified
If X and Y are two variables with σx = 3.8,σy = 4.2,and COV(X,Y)= −0.25,then V(X + Y)= 31.58.
COV
Coefficient of Variation, a statistical measure of the relative dispersion or variability in data, expressed as a percentage of the mean.
Variables
Elements, features, or factors that are likely to vary or change from one instance to another in a study or experiment.
- Familiarize with the rudimentary concepts and aspects concerning the addition of variances and expected values.
- Familiarize with and operationalize the concepts of covariance and correlation in relation to bivariate distributions.
Verified Answer
SJ
stella jiangabout 3 hours ago
Final Answer :
True
Explanation :
We can use the formula for the variance of the sum of two random variables:
V(X + Y) = V(X) + V(Y) + 2COV(X,Y)
Plugging in the given values:
V(X + Y) = σx + σy + 2COV(X,Y)
V(X + Y) = 3.8 + 4.2 + 2(-0.25)
V(X + Y) = 7.6 - 0.5
V(X + Y) = 7.1
Therefore, V(X + Y) = 31.58 is false, and the correct value is V(X + Y) = 7.1. So the answer is A.
V(X + Y) = V(X) + V(Y) + 2COV(X,Y)
Plugging in the given values:
V(X + Y) = σx + σy + 2COV(X,Y)
V(X + Y) = 3.8 + 4.2 + 2(-0.25)
V(X + Y) = 7.6 - 0.5
V(X + Y) = 7.1
Therefore, V(X + Y) = 31.58 is false, and the correct value is V(X + Y) = 7.1. So the answer is A.
Learning Objectives
- Familiarize with the rudimentary concepts and aspects concerning the addition of variances and expected values.
- Familiarize with and operationalize the concepts of covariance and correlation in relation to bivariate distributions.