Suppose that the random variables Y1 and Y2 have means ?1

Chapter 5, Problem 96E

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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.

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

  1. Cov(Y1,Y2) = Cov(Y2,Y1).
  2. Cov(Y1,Y1)= V(Y1) = .


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