1			Bayesian statistics is a branch of statistics that uses:
			A)	non-normal analysis
			B)	analysis using prior information
			C)	no hypothesis tests or confidence intervals
			D)	analysis by computer only
			E)	none of the above
2			The de Finetti game assesses:
			A)	personal probabilities
			B)	objective probabilities
			C)	gambling probabilities
			D)	game theory
			E)	none of the above
3			The utility function of a risk-averse person is:
			A)	concave
			B)	convex
			C)	straight line
			D)	s-shaped
			E)	none of the above
4			Suppose that you are sampling from a normal distribution with standard deviation 5. The population mean is assumed to be a random variable with mean 10 and standard deviation 3. A sample of size 100 gives a sample mean of 8. The posterior normal distribution of the population mean has a mean equal to:
			A)	0
			B)	10
			C)	5.389
			D)	2.932
			E)	none of the above
5			Suppose that you could buy a sure investment that gives 10% interest. You also have the option of buying an investment that gives 12% return with a 50% chance and an 8% return with a 50% chance. The expected monetary value of the sure investment is:
			A)	equal to that of the risky investment
			B)	greater than that of the risky investment
			C)	lesser than that of the risky investment
			D)	insufficient information to determine
			E)	zero

Use the following to answer questions 6-8:

A pharmaceutical company develops a new drug for a disease and expects it to have the following prior probability distribution of success based on laboratory tests. The partially completed posterior probability distribution of S is given.

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A random sample of ten patients revealed that four of them benefited from the drug.

6			Complete the table by giving the value of A.
			A)	0.205
			B)	0.377
			C)	0.172
			D)	0.246
			E)	none of the above
7			Complete the table by filling in the value of B.
			A)	0.0011
			B)	0.00055
			C)	0.5
			D)	0.022
			E)	none of the above
8			Complete the table by filling in the value of C.
			A)	0.000502
			B)	0.01998
			C)	0.0239
			D)	0.015075
			E)	none of the above
9			Subjective probabilities are:
			A)	Bayesian
			B)	posterior
			C)	prior
			D)	personal
			E)	none of the above
10			All the following are elements of a decision analysis, except:
			A)	actions
			B)	chance occurrences
			C)	final outcomes
			D)	subjective probabilities
			E)	decision

Use the following to answer questions 11-12:

A manager is trying to choose between options A, B & C. The value of each option depends on the state of nature that occurs well after the choice has been made. The likelihood of the two possible states of nature and the payoffs for the individual options are in the following table:

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11			Suppose this manager is so pessimistic that he always chooses the option whose worst-case scenario is most attractive. In this situation, how much does the manager's pessimism cost him (in terms of expected value)?
			A)	If the manager follows his usual approach, in this case he will pass up $7,200 in expected monetary value
			B)	If the manager follows his usual approach, in this case he will pass up $10,200 in expected monetary value
			C)	If the manager follows his usual approach, in this case he will pass up $10,000 in expected monetary value
			D)	If the manager follows his usual approach, in this case he will pass up $20,000 in expected monetary value
			E)	Nothing, because his decision-making approach would, in this case at least, lead to the optimal choice (in terms of expected monetary value)
12			In this situation, perfect information would be worth _____________ to this manager.
			A)	$ 50,000
			B)	$ 46,000
			C)	$ 29,200
			D)	$ 22,000
			E)	$ 16,800