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
+