Econometrics Problem Set: Statistical Concepts Review

METU
Department of Economics
Fall 2025-2026
Course:
ECON301 – Introduction to Econometrics I
Instructor:
Dilem Yıldırım
T.A.:
Duygu Çelik
Problem Set #1
Review of Statistical Concepts
Q1) Explain with a reason whether the following statements are true, false, or uncertain:
i)
Since the correlation between two variables, 𝑥 and 𝑦, can range from −1 to +1, this
also means that 𝑐𝑜𝑣(𝑥, 𝑦) also lies between these limits.
ii)
If the correlation between two variables is zero, it means that there is no relationship
between the two variables whatsoever.
Q2) Suppose that İlkin Aydın has a volleyball match at the weekend. Explain why her number of
points is properly viewed as a random variable.
Q3) Let 𝑌 be a random variable representing household income. Define the concepts of
the expected value 𝐸[𝑌] and the variance 𝑉𝑎𝑟(𝑌). Explain in words what each measure, and why
both are important when analyzing economic data.
Q4) For any two random variables 𝑥 and 𝑦, and constants 𝑎, 𝑏, 𝑐, and 𝑑; show that
𝑐𝑜𝑣(𝑎𝑥 + 𝑏, 𝑐𝑦 + 𝑑) = 𝑎𝑐 ∗ 𝑐𝑜𝑣(𝑥, 𝑦)
Q5) For any two random variables 𝑋 and 𝑌; show the variance of 𝑋 − 𝑌 in terms of the variance
of 𝑋, the variance of 𝑌, and the covariance of 𝑋 and 𝑌.
Q6) Show that
"
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q[(𝑥! − 𝑥̅ )(𝑦! − 𝑦s)] = tq 𝑥! 𝑦! u − 𝑛𝑥̅ 𝑦s
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