*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

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