Econ4261 Week 2 Math Question Paper

Kyoo il Kim Department of Economics University of Minnesota

Introduction to Econometrics, Econ4261 Spring 2013

P ROBLEM S ET 1 (D UE F EBRUARY 7, T HURSDAY IN CLASS )

Answer the Followings 1. Calculate: a) E[X], E[Y ] b) V ar[X], V ar[Y ] c) Cov[X, Y ] d) ρ(X, Y ) from the distribution below Y =1 X = 5000 X = 10, 000 X = 15, 000 0 1/8 1/3 Y =0 1/4 1/8 1/6 (1)

2. Suppose E[X] = 1 and E[Y ] = 2 and suppose X and Y are independent. Evaluate: a) E[2X + 1] b) E[X + Y ] c) E[X − 2Y ] d) E[XY + 1] 3. Suppose V ar[X] = 2, V ar[Y ] = 1, Cov[X, Y ] = 0. Evaluate: a) V ar[X + 2Y ] b) V ar[X − Y ] c) Cov[2X − Y, X − 1]
￿n
i=1 [Xi

4. Suppose c)

￿n

i=1 Xi

= 2 and

+ 2]

￿n

i=1 Yi

= 3. Evaluate: a)

￿n

i=1 [Xi

+