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Suppose that the random variables Y1 and Y2 have means ?1
Chapter 5, Problem 96E(choose chapter or problem)
Problem 96E
Suppose that the random variables Y1 and Y2 have means μ1 and μ2 and variances σ 21 and σ 22, respectively. Use the basic definition of the covariance of two random variables to establish that
a Cov(Y1, Y2) = Cov(Y2, Y1).
b Cov(Y1, Y1) = V (Y1) = σ 21 . That is, the covariance of a random variable and itself is just the variance of the random variable.
Questions & Answers
QUESTION:
Problem 96E
Suppose that the random variables Y1 and Y2 have means μ1 and μ2 and variances σ 21 and σ 22, respectively. Use the basic definition of the covariance of two random variables to establish that
a Cov(Y1, Y2) = Cov(Y2, Y1).
b Cov(Y1, Y1) = V (Y1) = σ 21 . That is, the covariance of a random variable and itself is just the variance of the random variable.
ANSWER:
Solution:
Step 1 of 2:
The random variables Y1 and Y2 have means and and variances and , respectively.
We have to show
- Cov(Y1,Y2) = Cov(Y2,Y1).
- Cov(Y1,Y1)= V(Y1) = .