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

Last Updated on February 10, 2019 by EssayPro