Solution Found!
Let X, Y, and Z be jointly distributed random variables.
Chapter 2, Problem 28E(choose chapter or problem)
QUESTION:
Let X, Y, and Z be jointly distributed random variables. Prove that \(\mathrm {Cov}(X+Y,Z)=\mathrm {Cov}(X,Z)+\mathrm {Cov}(Y,Z)\). (Hint: Use Equation 2.69.)
Equation Transcription:
Text Transcription:
Cov(X+Y,Z)=Cov(X,Z)+Cov(Y,Z)
Questions & Answers
QUESTION:
Let X, Y, and Z be jointly distributed random variables. Prove that \(\mathrm {Cov}(X+Y,Z)=\mathrm {Cov}(X,Z)+\mathrm {Cov}(Y,Z)\). (Hint: Use Equation 2.69.)
Equation Transcription:
Text Transcription:
Cov(X+Y,Z)=Cov(X,Z)+Cov(Y,Z)
ANSWER:
Solution :
Step 1 of 1:
Given X,Y, and Z be the jointly distributed random variable.
Our goal is :
a). We need to prove that Cov(X+Y,Z)=Cov(X,Z)+Cov(Y,Z).