Question

7. The Axiom of Distribution of Probabilities Across Alternatives (aka Frame Invariance) prevents what pathology of decision making? A. Inability to make choices under risk B. Neglecting base rates C. Manipulation by framing effects D. Obsession with infinitely improbable alternatives E. Becoming a "money pump" The following applies to questions 8-9 below. Consider the following sequential game (note Player 1's payoffs are in the upper right cells):

Answer 1

7. According to the question, option A is the correct option.

Basically, the axiom of distribution of probability across alternatives is expected utility or expected a payoff from given alternatives.

8.

	L L	L R	RL	RR
L	8 1	8 1	-1 3	-1 3
R	1 0	-5 -5	1 0	-5 -5

This is the normal form of the extensive form given in the question. for player 2 the dominant strategy is RL in terms of player 1.

10. It is rational. It follows from the rule of independence.

$A \succeq B \Leftrightarrow pA + (1-p) C \succeq p B + (1-p) C$

We apply this to question above:

$A \succeq B \Leftrightarrow pA \succeq p B$

$\Rightarrow pA + (1-p) B \succeq p B + (1-p) B$

$\Rightarrow pA + (1-p) B \succeq B$.

Hence proved.

11. The axiom of transitivity is violated as A>=B, C<B then A>C. In a question, it is given C>A which violates the rule of transitivity.

12. Likelihood ratio. To test the which model is more likely to fit in the data. This is used to evaluate p-value which helps us to accept or reject the null hypothesis against the alternative hypothesis (~H).

13, Events are independent.