Assignment #1: Probability & Statistics and Linear Regression
Question 1 (10 points)
X and Y are discrete random variables with the following joint distribution:
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:
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