1. The expected value of information is . . .

(a) the expected value with the information minus the expected value without the information.

(b) zero if the information does not change your decisions.

(c) the maximum you would be willing to pay for the information.

(d) all of the above.

(e) none of the above.

2. The IRS auditing staff is concerned with identifying potentially fraudulent tax returns. From past experience they believe that the probability of finding a fraudulent return given that the return contains deductions for charitable contributions exceeding the IRS standard is 20%. Given that the deductions for charitable contributions do not exceed the IRS standard, the probability of a fraudulent return decreases to 2%. If 8% of all returns exceed the IRS standard for deductions due to charitable contributions, what is the best estimate of the percentage of fraudulent returns?

(a) 1.60%

(b) 1.84%

(c) 3.44%

(d) 18.56%

(e) 20.00%

Consider the following simplified version of Universitystudent ratings of teaching effectiveness(SRTE). A student is asked to give the professor a rating on a scale of 1-7 with 7 being the best. Suppose Professor has, over his manyyears of teaching, received SRTE responses with the following probabilities.

Score	Prob.
1	.03
2	.05
3	.10
4	.10
5	.15
6	.35
7	.22

LetXdenote the rating from a randomlychosen student.

7. Find the expected value of X. please provide your answer with at least 2 decimals place of precision (e.g. X.XX).

8. Find the standard deviation of X.please provide your answer with at least 2 decimals place of precision (e.g. X.XX).