INTERMEDIATE ECONOMETRICS
Assignment #1: Probability & Statistics and Linear Regression
Question 1 (10 points)
X and Y are discrete random variables with the following joint distribution:
| Y | ||||
| 0 | 1 | 2 | ||
| X | 0 | 0.05 | 0.1 | 0.03 |
| 1 | 0.21 | 0.11 | 0.19 | |
| 2 | 0.08 | 0.15 | 0.08 |
That is, Pr (X = 0, Y = 0) = 0.05 and so on.
a) Compute the following probabilities:
| i. ii. | Prob[Y<2] Prob[Y<2,X>0] |
b) Find the marginal probability density functions for X and Y.
c) Calculate the mean and variance of X.
d) Calculate the conditional probability density function of Y given X=1, and the
conditional mean and variance of Y given X=1.
e) Calculate the covariance of X and Y.
f) Are X and Y independent? Explain.
Question 2 (5 points)
Consider the simple regression model