I
Answer one question [20%]
Q1) Given the joint probability distribution of two random variables X and Y
X
f(y)
y
1
2
3
.25
.25
4
.25
.25
f(x)
a) Fill in the blanks in the table above
b) Find E(X), V(X), Cov(X,Y), E(X\Y=3)
c) Are X and Y independent? Explain
d) Find V(X\Y=3)
Q2) Answer with true or false and explain with regard to the simple regression
a) The variance of the dependent variable does not equal the variance of the residual.
b) Given the assumptions of the classical linear model, OLS is BLUE
c) If the E(U\X<sub>i</sub>)=0 then E(Y<sub>i</sub>\X<sub>i</sub>) = a + b X<sub>i</sub>
d) The confidence interval of $\beta_2$ is
$pr(\hat{\beta}_2 - \delta \le \beta_2 \le \hat{\beta}_2 + \delta) = 1 - \alpha$
The above interval says that the probability lying between the said limits is 1-$\alpha$
e) The confidence interval in part d above is NOT RANDOM
f) Regression implies causation
