Vurderingsdokument:


Problem 1a)
- Setting up F_y(x,y) = P(X_min <= x, X_max <= y)  for x>=y         5 points
- Setting up F_y(x,y) = P(X_min <= x, X_max <= y)  for x<y          5 points

Problem 2a)
- Writing out a^T X = c							2 points
- Taking expectations after multiplication with X_1 			5 points
- Solving for rho and getting final result rho = -1/2			3 points

Problem 3a)								10 points
Problem 3b)
- Stating distribution function of X					3 points
- Understanding that X_1 = X_2 with probabality 1 			5 points
- Finding solution							2 points

Problem 4a)

Deriving R-squared							4 points
Deriving degrees of freedom for F-statistic				3 + 3 points

Problem 4b)
Definition of test statistic						4 points
Finding value for F							3 points
Finding critical value plus conclusion					3 points

Problem 4c)
Solution for Bonferroni							5 points
Solution for Sidak							5 points

Problem 4d)		
Finding test statistic							3 points
Finding critical value under chi-squared distribution			4 points
Conclusion								3 points

Problem 5a) 
Expression for g(y)							5 points
Finding solution for g(y) for specific case given			5 points

Problem 6a)
Finding distribution for ratio						5 points
Finiding probability							5 points