ECON2280_2018_sem1_Tutorial 1 PS.pdf - ECON2280 Introductory Econometrics Tutorial 1 Tutorial 1 Problem set Question 1(Review of Statistics Here is the

ECON2280_2018_sem1_Tutorial 1 PS.pdf - ECON2280...

This preview shows page 1 - 3 out of 3 pages.

ECON2280 Introductory Econometrics Tutorial 1 Tutorial 1 Problem set Question 1 (Review of Statistics) Here is the table describing the joint distribution of the random variable X and Y. Pr ( X = x; Y = y ) Y = 4 Y = 9 X = 1 0.24 0.16 X = 2 0.12 0.08 X = 4 0.24 0.16 1. Calculate the marginal probability of X and the marginal probability of Y. 2. Find E ( X ) and E ( Y ) : 3. Find V ar ( X ) and V ar ( Y ) : 4. De°ne a new random variable Z = XY: Find out the distribution of Z . 5. Find E ( Z ) and V ar ( Z ) : 6. Based on the joint probabilities and the marginal probabilities, are X and Y independent of each other? 7. Find Cov ( X; Y ) using (a) the formula Cov ( X; Y ) = E [( X ° E ( X )) ( Y ° E ( Y ))] : 1 1. P(X=1) = 0.24+0.16 = 0.4 P(X=2) = 0.12+0.08 = 0.2 P(X=4) = 0.24+0.16 = 0.4 P(Y=4) = 0.24+0.12+0.24=0.6 P(Y=9) = 0.16+0.08+0.16=0.4 2. E(X)= 1x0.4 +2x0.2 +4x0.4 =2.4 E(Y)= 4x0.6 + 9x0.4= 6 3. Var(X)= 0.4x(1-2.4)^(2) + 0.2x(2-2.4)^(2) + 0.4x(4-2.4)^(2)= 1.84 Var(Y) = 0.6x(4-6)^(2) + 0.4x(9-6)^(2) = 6
Image of page 1

Subscribe to view the full document.

(b) the formula Cov ( X; Y ) = E ( XY ) ° E ( X ) E ( Y ) : 8. Find Corr ( X; Y ) 9. Find E ( X j Y = 4) ; E ( Y j X = 4) ; V ar ( X j Y = 4) ; V ar ( Y j X = 4) : 10. Find the conditional probabilities of Y given Z > 8 ; i:e:; Pr ( Y = 4 j Z > 8) and Pr ( Y = 9 j Z > 8) , where Z = XY: Question 2 1. Using the fact that
Image of page 2
Image of page 3

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes