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ECN224 Econometrics I – 2016
Questions and Answers
Question 1
a)
The integral of the probability density function of a random variable must equal one. Therefore, we
can integrate this over x and y as follows:
𝑥𝑦
1 = 𝑐𝑥 + 𝑑𝑦 𝑑𝑥
3
𝑥
1 = [𝑐𝑦𝑥 + 𝑦 ] 𝑑𝑥
6
2𝑥
1 = 2𝑐𝑥 + 𝑑𝑥
3
2 𝑥
1 = [ 𝑐𝑥 + ]
3 3
2 1
1 = 𝑐 +
3 3
𝑐 = 1
b) To find the marginal pdf’s, we integrate against y to find the x-marginal, and integrate against x to
find the y-marginal:
ECONOMICS HELP, visit LondonEconomicsTutors.co.uk.
Discounted prices compared to all other websites
ECN224 Econometrics I – 2016
Questions and Answers
Question 1
a)
The integral of the probability density function of a random variable must equal one. Therefore, we
can integrate this over x and y as follows:
𝑥𝑦
1 = 𝑐𝑥 + 𝑑𝑦 𝑑𝑥
3
𝑥
1 = [𝑐𝑦𝑥 + 𝑦 ] 𝑑𝑥
6
2𝑥
1 = 2𝑐𝑥 + 𝑑𝑥
3
2 𝑥
1 = [ 𝑐𝑥 + ]
3 3
2 1
1 = 𝑐 +
3 3
𝑐 = 1
b) To find the marginal pdf’s, we integrate against y to find the x-marginal, and integrate against x to
find the y-marginal:
