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1. If a random variable X is distributed chi square with n degrees of freedom then the expected value of X is n. Show that this is true.
2. Suppose we have a random sample X1, X2, ...Xn from a distribution with mean µ and variance σ2. Let's compare two estimators in terms of their relative efficiency. The first estimator is the sample mean Xbar. The second estimator is the second observation in the sample, X2. Which one is more efficient? (hint: calculate the expected value and variance of both)
3. You are given the following information about the joint probability distribution of X and Y:
Y=1
Y=2
Y=3
X=0
0.25
0.1
0.05
X=1
0.3
0.2
Determine the following:
Design a simple econometric research project
Multiplicative decomposition method
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Explain why this model violates the assumption of no perfect collinearity. Write the t statistic for testing the null hypothesis
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