Consider the monthly returns of two risky assets. The return of the first asset has a mean of 2% and standard deviation of 3%. The return of the second asset has a mean of 1.5% and standard deviation of 2%. The correlation coefficient of the two returns is 0.3. How can the minimum variance portfolio (MVP) be constructed? What are the mean and standard deviation of the return of the MVP? Consider a portfolio with 50% invested in asset 1 and 50% invested in asset 2. Is such a portfolio efficient?

When the transportation of natural gas in a pipeline is not feasible for economic
reasons, it is first liquefied using nonconventional refrigeration techniques and
then transported in super-insulated tanks. In a natural gas liquefaction plant,
the liquefied natural gas (LNG) enters a cryogenic turbine at 3 MPa and -160
°C at a rate of 20 kg/s and leaves at 0.3 MPa. If 115 kW power is produced by
the turbine, determine the efficiency of the turbine. Take the density of LNG to
be 423.8 kg/m3

Example #2A block with mass m = 5 kg sits on a surface with a coefficient of static friction sk= 0.5 and a coefficient of kinetic friction uk= 0.3. a)If you can pull on the block at any angle, what minimum force is required to break static friction and cause the block to slide? b)What is the optimal angle to pull at? c)If you pull at the optimal angle with the minimum force, what will the acceleration of the block be once static friction is broken?

(Bonus question) Are coffee drinkers more likely to suffer from high blood pressure? For a random sample of 50 coffee drinkers, 30 had high blood pressure. In a random sample of 50 non-coffee drinkers, 25 had high blood pressure. Let p1, p2 denote the population proportion of high blood pressure among coffee drinkers and non-coffee drinkers respectively.

1. (a) Construct a 95% CI for the difference between these two proportions p1 − p2. (3pts).

2. (b) Someone proposes that coffee drinkers have higher proportion of high blood pressure than non-coffee drinkers. Test the claim at 0.05 significance level. Give the H0,Ha, test statistics, p-value and conclusion. (3pts)

Table A: Standard Normal Distribution. Table entry is P[Z < z]

z 0.00 -3.4 0.0003 -3.3 0.0005 -3.2 0.0007 -3.1 0.0010 -3.0 0.0013 -2.9 0.0019 -2.8 0.0026 -2.7 0.0035 -2.6 0.0047 -2.5 0.0062 -2.4 0.0082 -2.3 0.0107 -2.2 0.0139 -2.1 0.0179 -2.0 0.0228 -1.9 0.0287 -1.8 0.0359 -1.7 0.0446 -1.6 0.0548 -1.5 0.0668 -1.4 0.0808 -1.3 0.0968 -1.2 0.1151 -1.1 0.1357 -1.0 0.1587 -0.9 0.1841 -0.8 0.2119 -0.7 0.2420 -0.6 0.2743 -0.5 0.3085 -0.4 0.3446 -0.3 0.3821 -0.2 0.4207 -0.1 0.4602 -0.0 0.5000

0. 0.0 0.5000

1. 0.1 0.5398

2. 0.2 0.5793

3. 0.3 0.6179

4. 0.4 0.6554

5. 0.5 0.6915

6. 0.6 0.7257

7. 0.7 0.7580

8. 0.8 0.7881

9. 0.9 0.8159

0. 1.0 0.8413

1. 1.1 0.8643

2. 1.2 0.8849

3. 1.3 0.9032

4. 1.4 0.9192

5. 1.5 0.9332

6. 1.6 0.9452

7. 1.7 0.9554

8. 1.8 0.9641

9. 1.9 0.9713

0. 2.0 0.9772

1. 2.1 0.9821

2. 2.2 0.9861

3. 2.3 0.9893

4. 2.4 0.9918

5. 2.5 0.9938

6. 2.6 0.9953

7. 2.7 0.9965

8. 2.8 0.9974

9. 2.9 0.9981

0. 3.0 0.9987

1. 3.1 0.9990

2. 3.2 0.9993

3. 3.3 0.9995

4. 3.4 0.9997

0.01 0.02 0.03 0.0003 0.0003 0.0003 0.0005 0.0005 0.0004 0.0007 0.0006 0.0006 0.0009 0.0009 0.0009 0.0013 0.0013 0.0012 0.0018 0.0018 0.0017 0.0025 0.0024 0.0023 0.0034 0.0033 0.0032 0.0045 0.0044 0.0043 0.0060 0.0059 0.0057 0.0080 0.0078 0.0075 0.0104 0.0102 0.0099 0.0136 0.0132 0.0129 0.0174 0.0170 0.0166 0.0222 0.0217 0.0212 0.0281 0.0274 0.0268 0.0351 0.0344 0.0336 0.0436 0.0427 0.0418 0.0537 0.0526 0.0516 0.0655 0.0643 0.0630 0.0793 0.0778 0.0764 0.0951 0.0934 0.0918 0.1131 0.1112 0.1093 0.1335 0.1314 0.1292 0.1562 0.1539 0.1515 0.1814 0.1788 0.1762 0.2090 0.2061 0.2033 0.2389 0.2358 0.2327 0.2709 0.2676 0.2643 0.3050 0.3015 0.2981 0.3409 0.3372 0.3336 0.3783 0.3745 0.3707 0.4168 0.4129 0.4090 0.4562 0.4522 0.4483 0.4960 0.4920 0.4880 0.5040 0.5080 0.5120 0.5438 0.5478 0.5517 0.5832 0.5871 0.5910 0.6217 0.6255 0.6293 0.6591 0.6628 0.6664 0.6950 0.6985 0.7019 0.7291 0.7324 0.7357 0.7611 0.7642 0.7673 0.7910 0.7939 0.7967 0.8186 0.8212 0.8238 0.8438 0.8461 0.8485 0.8665 0.8686 0.8708 0.8869 0.8888 0.8907 0.9049 0.9066 0.9082 0.9207 0.9222 0.9236 0.9345 0.9357 0.9370 0.9463 0.9474 0.9484 0.9564 0.9573 0.9582 0.9649 0.9656 0.9664 0.9719 0.9726 0.9732 0.9778 0.9783 0.9788 0.9826 0.9830 0.9834 0.9864 0.9868 0.9871 0.9896 0.9898 0.9901 0.9920 0.9922 0.9925 0.9940 0.9941 0.9943 0.9955 0.9956 0.9957 0.9966 0.9967 0.9968 0.9975 0.9976 0.9977 0.9982 0.9982 0.9983 0.9987 0.9987 0.9988 0.9991 0.9991 0.9991 0.9993 0.9994 0.9994 0.9995 0.9995 0.9996 0.9997 0.9997 0.9997

0.04 0.05 0.0003 0.0003 0.0004 0.0004 0.0006 0.0006 0.0008 0.0008 0.0012 0.0011 0.0016 0.0016 0.0023 0.0022 0.0031 0.0030 0.0041 0.0040 0.0055 0.0054 0.0073 0.0071 0.0096 0.0094 0.0125 0.0122 0.0162 0.0158 0.0207 0.0202 0.0262 0.0256 0.0329 0.0322 0.0409 0.0401 0.0505 0.0495 0.0618 0.0606 0.0749 0.0735 0.0901 0.0885 0.1075 0.1056 0.1271 0.1251 0.1492 0.1469 0.1736 0.1711 0.2005 0.1977 0.2296 0.2266 0.2611 0.2578 0.2946 0.2912 0.3300 0.3264 0.3669 0.3632 0.4052 0.4013 0.4443 0.4404 0.4840 0.4801 0.5160 0.5199 0.5557 0.5596 0.5948 0.5987 0.6331 0.6368 0.6700 0.6736 0.7054 0.7088 0.7389 0.7422 0.7704 0.7734 0.7995 0.8023 0.8264 0.8289 0.8508 0.8531 0.8729 0.8749 0.8925 0.8944 0.9099 0.9115 0.9251 0.9265 0.9382 0.9394 0.9495 0.9505 0.9591 0.9599 0.9671 0.9678 0.9738 0.9744 0.9793 0.9798 0.9838 0.9842 0.9875 0.9878 0.9904 0.9906 0.9927 0.9929 0.9945 0.9946 0.9959 0.9960 0.9969 0.9970 0.9977 0.9978 0.9984 0.9984 0.9988 0.9989 0.9992 0.9992 0.9994 0.9994 0.9996 0.9996 0.9997 0.9997

0.06 0.07 0.0003 0.0003 0.0004 0.0004 0.0006 0.0005 0.0008 0.0008 0.0011 0.0011 0.0015 0.0015 0.0021 0.0021 0.0029 0.0028 0.0039 0.0038 0.0052 0.0051 0.0069 0.0068 0.0091 0.0089 0.0119 0.0116 0.0154 0.0150 0.0197 0.0192 0.0250 0.0244 0.0314 0.0307 0.0392 0.0384 0.0485 0.0475 0.0594 0.0582 0.0721 0.0708 0.0869 0.0853 0.1038 0.1020 0.1230 0.1210 0.1446 0.1423 0.1685 0.1660 0.1949 0.1922 0.2236 0.2206 0.2546 0.2514 0.2877 0.2843 0.3228 0.3192 0.3594 0.3557 0.3974 0.3936 0.4364 0.4325 0.4761 0.4721 0.5239 0.5279 0.5636 0.5675 0.6026 0.6064 0.6406 0.6443 0.6772 0.6808 0.7123 0.7157 0.7454 0.7486 0.7764 0.7794 0.8051 0.8078 0.8315 0.8340 0.8554 0.8577 0.8770 0.8790 0.8962 0.8980 0.9131 0.9147 0.9279 0.9292 0.9406 0.9418 0.9515 0.9525 0.9608 0.9616 0.9686 0.9693 0.9750 0.9756 0.9803 0.9808 0.9846 0.9850 0.9881 0.9884 0.9909 0.9911 0.9931 0.9932 0.9948 0.9949 0.9961 0.9962 0.9971 0.9972 0.9979 0.9979 0.9985 0.9985 0.9989 0.9989 0.9992 0.9992 0.9994 0.9995 0.9996 0.9996 0.9997 0.9997

0.08 0.09 0.0003 0.0002 0.0004 0.0003 0.0005 0.0005 0.0007 0.0007 0.0010 0.0010 0.0014 0.0014 0.0020 0.0019 0.0027 0.0026 0.0037 0.0036 0.0049 0.0048 0.0066 0.0064 0.0087 0.0084 0.0113 0.0110 0.0146 0.0143 0.0188 0.0183 0.0239 0.0233 0.0301 0.0294 0.0375 0.0367 0.0465 0.0455 0.0571 0.0559 0.0694 0.0681 0.0838 0.0823 0.1003 0.0985 0.1190 0.1170 0.1401 0.1379 0.1635 0.1611 0.1894 0.1867 0.2177 0.2148 0.2483 0.2451 0.2810 0.2776 0.3156 0.3121 0.3520 0.3483 0.3897 0.3859 0.4286 0.4247 0.4681 0.4641 0.5319 0.5359 0.5714 0.5753 0.6103 0.6141 0.6480 0.6517 0.6844 0.6879 0.7190 0.7224 0.7517 0.7549 0.7823 0.7852 0.8106 0.8133 0.8365 0.8389 0.8599 0.8621 0.8810 0.8830 0.8997 0.9015 0.9162 0.9177 0.9306 0.9319 0.9429 0.9441 0.9535 0.9545 0.9625 0.9633 0.9699 0.9706 0.9761 0.9767 0.9812 0.9817 0.9854 0.9857 0.9887 0.9890 0.9913 0.9916 0.9934 0.9936 0.9951 0.9952 0.9963 0.9964 0.9973 0.9974 0.9980 0.9981 0.9986 0.9986 0.9990 0.9990 0.9993 0.9993 0.9995 0.9995 0.9996 0.9997 0.9997 0.9998

6

Table C: t distribution critical values Table entries are t∗ values for confidence level C 1-sided and 2-sided P-values are also shown

Confidence Level C

7

df 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 35 40 45 50 z∗

1-sided P 2-sided P

50% 60% 80% 1.0000 1.3764 3.0777 0.8165 1.0607 1.8856 0.7649 0.9785 1.6377 0.7407 0.9410 1.5332 0.7267 0.9195 1.4759 0.7176 0.9057 1.4398 0.7111 0.8960 1.4149 0.7064 0.8889 1.3968 0.7027 0.8834 1.3830 0.6998 0.8791 1.3722 0.6974 0.8755 1.3634 0.6955 0.8726 1.3562 0.6938 0.8702 1.3502 0.6924 0.8681 1.3450 0.6912 0.8662 1.3406 0.6901 0.8647 1.3368 0.6892 0.8633 1.3334 0.6884 0.8620 1.3304 0.6876 0.8610 1.3277 0.6870 0.8600 1.3253 0.6864 0.8591 1.3232 0.6858 0.8583 1.3212 0.6853 0.8575 1.3195 0.6848 0.8569 1.3178 0.6844 0.8562 1.3163 0.6840 0.8557 1.3150 0.6837 0.8551 1.3137 0.6834 0.8546 1.3125 0.6830 0.8542 1.3114 0.6828 0.8538 1.3104 0.6816 0.8520 1.3062 0.6807 0.8507 1.3031 0.6800 0.8497 1.3006 0.6794 0.8489 1.2987

0.674 0.841 1.282 0.25 0.20 0.10 0.50 0.40 0.20

90% 95% 6.3138 12.706 2.9200 4.3027 2.3534 3.1824 2.1318 2.7764 2.0150 2.5706 1.9432 2.4469 1.8946 2.3646 1.8595 2.3060 1.8331 2.2622 1.8125 2.2281 1.7959 2.2010 1.7823 2.1788 1.7709 2.1604 1.7613 2.1448 1.7531 2.1314 1.7459 2.1199 1.7396 2.1098 1.7341 2.1009 1.7291 2.0930 1.7247 2.0860 1.7207 2.0796 1.7171 2.0739 1.7139 2.0687 1.7109 2.0639 1.7081 2.0595 1.7056 2.0555 1.7033 2.0518 1.7011 2.0484 1.6991 2.0452 1.6973 2.0423 1.6896 2.0301 1.6839 2.0211 1.6794 2.0141 1.6759 2.0086

1.645 1.96 0.05 0.025 0.10 0.05

96% 98% 99% 99.8% 15.895 31.821 63.657 318.31 4.8487 6.9646 9.9248 22.327 3.4819 4.5407 5.8409 10.215 2.9985 3.7469 4.6041 7.1732 2.7565 3.3649 4.0321 5.8934 2.6122 3.1427 3.7074 5.2076 2.5168 2.9980 3.4995 4.7853 2.4490 2.8965 3.3554 4.5008 2.3984 2.8214 3.2498 4.2968 2.3593 2.7638 3.1693 4.1437 2.3281 2.7181 3.1058 4.0247 2.3027 2.6810 3.0545 3.9296 2.2816 2.6503 3.0123 3.8520 2.2638 2.6245 2.9768 3.7874 2.2485 2.6025 2.9467 3.7328 2.2354 2.5835 2.9208 3.6862 2.2238 2.5669 2.8982 3.6458 2.2137 2.5524 2.8784 3.6105 2.2047 2.5395 2.8609 3.5794 2.1967 2.5280 2.8453 3.5518 2.1894 2.5176 2.8314 3.5272 2.1829 2.5083 2.8188 3.5050 2.1770 2.4999 2.8073 3.4850 2.1715 2.4922 2.7969 3.4668 2.1666 2.4851 2.7874 3.4502 2.1620 2.4786 2.7787 3.4350 2.1578 2.4727 2.7707 3.4210 2.1539 2.4671 2.7633 3.4082 2.1503 2.4620 2.7564 3.3962 2.1470 2.4573 2.7500 3.3852 2.1332 2.4377 2.7238 3.3400 2.1229 2.4233 2.7045 3.3069 2.1150 2.4121 2.6896 3.2815 2.1087 2.4033 2.6778 3.2614

2.054 2.326 2.576 3.091 0.02 0.01 0.005 0.001 0.04 0.02 0.01 0.002

99.9% 636.62 31.599 12.924 8.6103 6.8688 5.9588 5.4079 5.0413 4.7809 4.5869 4.4370 4.3178 4.2208 4.1405 4.0728 4.0150 3.9651 3.9216 3.8834 3.8495 3.8193 3.7921 3.7676 3.7454 3.7251 3.7066 3.6896 3.6739 3.6594 3.6460 3.5911 3.5510 3.5203 3.4960

3.291 0.0005 0.001

A recent study in the Journal of Consumer Research suggests that appetite stimuli can make people more impatient in unrelated areas. Participants in the study, all college students, were asked to serve as photo editors for a magazine. Half were randomly selected to view appetite-stimulating pictures of desserts, and the other half viewed non-appetite-stimulating nature pictures. Then the participants were offered a choice between an apartment with a great view and an apartment close to work. The apartment with a great view is the impatient option because it’s associated with more immediate (less delayed) benefits than the apartment close to work. [Source: Li, X. (2008). The effects of appetitive stimuli on out-of-domain consumption impatience. Journal of Consumer Research, 34.]

A total of 65% of the students who viewed dessert photographs picked the apartment with a great view, while 60% of the students who viewed nature photographs chose this option.

Consider this experiment: The study is rerun on a randomly selected college student.

The following tree diagram depicts the process of the student being randomly assigned to view either dessert or nature pictures (Step 1) and his or her subsequent choice between the apartment with a great view and the apartment close to work (Step 2).

Find the values of the three designated probabilities, and enter them in the following table (round probabilities to two decimal places).

What is the probability that the randomly selected student picks the apartment with a great view?

0.375

0.5

0.975

0.625

What is the prior probability that the randomly selected student viewed nature pictures?

0.6

0.8

0.3

0.5

Now use the information that the student picked the apartment with a great view to compute the posterior probability that the student viewed nature pictures. The posterior probability is   .

Given the information that the student picked the apartment with a great view, what’s the posterior probability that the student viewed dessert pictures?

0.33

0.30

1.92

0.52

You hold a portfolio with the following securities:

The expected portfolio return is  Blank 1. Calculate the answer by read surrounding text. %. Round to the nearest 0.01% (drop the % symbol). E.g., if your answer is 21.93%, record it as 21.93.

Refer to the table below:

Using the information provided on the two stocks in the table above, find the expected return on the minimum variance portfolio. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Please explain how: A sample contains MgNH4(PO4)2, Sb2S3, KBr, Cr(OH)3, and PbCl2. Identify the soluble ions after the addition of 6 M HCl; then H2S and 0.2 M HCl; then OH- to a pH of 8; and then (NH4)2HPO4 with NH3. Explain. a.) Sb2S3 b.) KBr c.) PbCl2 d.) Cr(OH)3 e.) MgNH4(PO4)2

A multiple-choice examination consists of

85

questions, each having possible choices a, b, c, d, and e. Approximate the probability that a student will get at most

18

answers correct if she randomly guesses at each answer. (Note that, if she randomly guesses at each answer, then the probability that she gets any one answer correct is 0.2.) Use the normal approximation to the binomial with a correction for continuity.