1a) Will students who perform very badly on Test 1 tend to perform less badly on Test 2?(4 marks)

• Yes
• No

1b) What's the statistical phenomenon behind this? (6 marks)

1. Simpson paradox
2. Berkson paradox
3. Regression to the mean
4. Maximum likelihood

2)Sarah is considering playing a game with a fair die. Suppose you will win a prize of 300 if the number of 6 is rolled, 200 if the number of 5 is rolled, and 0 for the rest. Playing the game costs 90.

2a) What is the total expected utility of Sarah's decision to play the game? Should Sarah play the game? (7 marks)

2b) If Sarah values the excitement of playing the game as having a utility of 6. What is the total expected utility of Sarah's decision to play the game? Should Sarah play the game? (8 marks)