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ECN224 Econometrics 1 – 2014
Questions and Answers
Question 1
a)
𝑐𝑜𝑣(𝑥, 𝑧)
𝑐𝑜𝑟𝑟(𝑥, 𝑧) =
𝑣𝑎𝑟(𝑥) 𝑣𝑎𝑟(𝑧)
𝑐𝑜𝑣(𝑥, 𝑧)
−2 =
√4√16
−2 × 2 × 4 = 𝑐𝑜𝑣(𝑥, 𝑧)
−16 = 𝑐𝑜𝑣(𝑥, 𝑧)
b)
𝑐𝑜𝑣(𝑥, 𝑦)
𝑐𝑜𝑟𝑟(𝑥, 𝑦) =
𝑣𝑎𝑟(𝑥) 𝑣𝑎𝑟(𝑦)
𝑐𝑜𝑣(𝑥, 𝑦)
3 =
√4√9
3 × 2 × 3 = 𝑐𝑜𝑣(𝑥, 𝑦)
18 = 𝑐𝑜𝑣(𝑥, 𝑦)
c)
𝑐𝑜𝑣(4𝑥 + 2𝑦, 3𝑥 − 4𝑧) = 𝑐𝑜𝑣(4𝑥, 3𝑥 − 4𝑧) + 𝑐𝑜𝑣(2𝑦, 3𝑥 − 4𝑧)
= 𝑐𝑜𝑣(4𝑥, 3𝑥 − 4𝑧) + 𝑐𝑜𝑣(2𝑦, 3𝑥 − 4𝑧)
= 𝑐𝑜𝑣(4𝑥, 3𝑥) + 𝑐𝑜𝑣(4𝑥, −4𝑧) + 𝑐𝑜𝑣(2𝑦, 3𝑥) + 𝑐𝑜𝑣(2𝑦, −4𝑧)
= 12 𝑣𝑎𝑟(𝑥) − 16𝑐𝑜𝑣(𝑥, 𝑧) + 6𝑐𝑜𝑣(𝑦, 𝑥) − 8𝑐𝑜𝑣(𝑦, 𝑧)
= 12(4) − 16(−16) + 6(18) − 8(0)
= 12(4) − 16(−16) + 6(18) − 8(0) = 412