economics honours
DC-1
Sem-II
Chapter: Covariance and Correlation
Content Developers: Vaishali Kapoor & Rakhi
Arora
College / University: Rajdhani College
(University of Delhi)
Institute of Lifelong Learning, University of Delhi
1
Table of Contents
1. Learning outcomes
2. Introduction
3. Covariance
a. Discrete Random Variable
b. Continuous Random Variable
c. Special cases
4. Correlation
5. Appendix
6. Summary
7. Exercises
8. Glossary
9. References
Institute of Lifelong Learning, University of Delhi
2
Learning outcomes
After you have read this chapter, you should be able to:1. Define Covariance.
2. Calculate the covariance for the discrete and Continuous Random
Variables.
3. Consider the special cases of covariance.
4. Compute correlation.
Institute of Lifelong Learning, University of Delhi
3
Introduction
So far we have studied Joint Probability mass / Density function and expected value of some function of random variables. It is also of interested, at times, to know whether two random variables have some sort of relationship or not. For example, someone may be interested in knowing whether marks obtained by a student is positively affected by number of hours denoted to studying by that student or is negatively affected by hours denoted to watching
T.V. If X is marks obtained and Y is number of hours daily spent on studying, then one is interested in knowing whether X and Y are related. If Yes, positively or negatively (the answer we expect is positive) and if it do affect, how strongly are they related.
For answering the above question, we need to learn statistical techniques of covariance and correlation. This chapter aids is understanding these and solving through these techniques. First section of this chapter covers covariance for discrete and continuous random variables and various theorems and its proofs and corollaries are covered. Second section of this chapter focuses on measuring strength of
Sem-II
Chapter: Covariance and Correlation
Content Developers: Vaishali Kapoor & Rakhi
Arora
College / University: Rajdhani College
(University of Delhi)
Institute of Lifelong Learning, University of Delhi
1
Table of Contents
1. Learning outcomes
2. Introduction
3. Covariance
a. Discrete Random Variable
b. Continuous Random Variable
c. Special cases
4. Correlation
5. Appendix
6. Summary
7. Exercises
8. Glossary
9. References
Institute of Lifelong Learning, University of Delhi
2
Learning outcomes
After you have read this chapter, you should be able to:1. Define Covariance.
2. Calculate the covariance for the discrete and Continuous Random
Variables.
3. Consider the special cases of covariance.
4. Compute correlation.
Institute of Lifelong Learning, University of Delhi
3
Introduction
So far we have studied Joint Probability mass / Density function and expected value of some function of random variables. It is also of interested, at times, to know whether two random variables have some sort of relationship or not. For example, someone may be interested in knowing whether marks obtained by a student is positively affected by number of hours denoted to studying by that student or is negatively affected by hours denoted to watching
T.V. If X is marks obtained and Y is number of hours daily spent on studying, then one is interested in knowing whether X and Y are related. If Yes, positively or negatively (the answer we expect is positive) and if it do affect, how strongly are they related.
For answering the above question, we need to learn statistical techniques of covariance and correlation. This chapter aids is understanding these and solving through these techniques. First section of this chapter covers covariance for discrete and continuous random variables and various theorems and its proofs and corollaries are covered. Second section of this chapter focuses on measuring strength of