1. A card is drawn at random from an ordinary deck of 52 playing cards. Describe the sample space if consideration of suits (a) is not, (b) is, taken into account.

2. Answer for b: both a king and a club = king of club.

3. A fair die is tossed twice. Find the probability of getting a 4, 5, or 6 on the first toss and a 1, 2, 3, or 4 on the second toss.

4. Find the probability of not getting a 7 or 11 total on either of two tosses of a pair of fair dice.

5. Two cards are drawn from a well-shuffled ordinary deck of 52 cards. Find the probability that they are both aces if the first card is (a) replaced, (b) not replaced.

6 Find the probability of a 4 turning up at least once in two tosses of a fair die.

7. One bag contains 4 white balls and 2 black balls; another contains 3 white balls and 5 black balls. If one ball is drawn from each bag, find the probability that (a) both are white, (b) both are black,(c) one is white and one is black.

8. Box I contains 3 red and 2 blue marbles while Box II contains 2 red and 8 blue marbles. A fair coin is tossed. If the coin turns up heads, a marble is chosen from Box I; if it turns up tails, a marble is chosen from Box II. Find the probability that a red marble is chosen.

9. A committee of 3 members is to be formed consisting of one representative each from labor, management, and the public. If there are 3 possible representatives from labor,2 from management, and 4 from the public, determine how many different committees can be formed

10. In how many ways can 5 differently colored marbles be arranged in a row?

11. In how many ways can 10 people be seated on a bench if only 4 seats are available?

12.. It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

13. How many 4-digit numbers can be formed with the 10 digits 0,1,2,3,. . . ,9 if (a) repetitions are allowed, (b) repetitions are not allowed, (c) the last digit must be zero and repetitions are not allowed?

14. Four different mathematics books, six different physics books, and two different chemistry books are to be arranged on a shelf. How many different arrangements are possible if (a) the books in each particular subject must all stand together, (b) only the mathematics books must stand together?

15. Five red marbles, two white marbles, and three blue marbles are arranged in a row. If all the marbles of the same color are not distinguishable from each other, how many different arrangements are possible?

16. In how many ways can 7 people be seated at a round table if (a) they can sit anywhere,(b) 2 particular people must not sit next to each other?

17. In how many ways can 10 objects be split into two groups containing 4 and 6 objects, respectively?

18. In how many ways can a committee of 5 people be chosen out of 9 people?

19. Out of 5 mathematicians and 7 physicists, a committee consisting of 2 mathematicians and 3 physicists is to be formed. In how many ways can this be done if (a) any mathematician and any physicist can be included, (b) one particular physicist must be on the committee, (c) two particular mathematicians cannot be on the committee?

20. How many different salads can be made from lettuce, escarole, endive, watercress, and chicory?

21. From 7 consonants and 5 vowels,how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning.

22. In the game of poker5 cards are drawn from a pack of 52 well-shuffled cards. Find the probability that (a) 4 are aces, (b) 4 are aces and 1 is a king, (c) 3 are tens and 2 are jacks, (d) a nine, ten, jack, queen, king are obtained in any order, (e) 3 are of any one suit and 2 are of another, (f) at least 1 ace is obtained.

23. Determine the probability of three 6s in 5 tosses of a fair die.

24. A shelf has 6 mathematics books and 4 physics books. Find the probability that 3 particular mathematics books will be together.

25. A and B play 12 games of chess of which 6 are won by A,4 are won by B,and 2 end in a draw. They agree to play a tournament consisting of 3 games. Find the probability that (a) A wins all 3 games, (b) 2 games end in a draw, (c) A and B win alternately, (d) B wins at least 1 game.

26. A and B play a game in which they alternately toss a pair of dice. The one who is first to get a total of 7 wins the game. Find the probability that (a) the one who tosses first will win the game, (b) the one who tosses second will win the game.

27. A machine produces a total of 12,000 bolts a day, which are on the average 3% defective. Find the probability that out of 600 bolts chosen at random, 12 will be defective.

28. The probabilities that a husband and wife will be alive 20 years from now are given by 0.8 and 0.9, respectively. Find the probability that in 20 years (a) both, (b) neither, (c) at least one, will be alive.

Q3. Spot rate, forward rate, and yield to maturity One year zero priced at 5% yield. Two year 6% coupon bond priced at par. Three year 7% coupon par priced at par.

a. what is one year, two year AND three year spot rates (ie s1 s2 s3)?

b. what is the 1 year and 2 year forward rate (ie f12 f23)?

c. How much should a THREE year 10% coupon bond with face value of $1,000 be price at?

d. What is the yield to maturity for bond in part 3c (4 points)?

4. Mortgage Pricing A 30Y fixed rate mortgage is issued at 6% coupon rate. The loan fully amortizes over 30 year period. Expected payoff time is 8 Years when initially issued. Assuming $1M in loan balance.

a. Price the loan today at 5%, 6%, and 7% market yield, assuming loan termination term stays constant with interest rate (96 months at 5%; 96 months at 6%, and 96 months @ 7% ).

b. calculate numerical duration and convexity at 6% market interest rate based on pricing from

4a c. Price the loan today at 5%, 6%, and 7% yield, assuming loan termination term changes with interest rate (60 months at 5%; 120 months at 6%, and extends to 120 months @ 7% ).

b. calculate numerical duration and convexity at 6% market interest rate based on pricing from 4a

7

(a) Distinguish/Define the following Barriers to International Trade                                              Tariff-Barrier: _____       Non-Tariff Barrier (NTB): ______                                                           (b) True/False? _____ The objectives of both Tariff- barrier & Non-tariff barrier are the same as they both help to positively manage international trade and global growth.                                         (c) What are the 2 countries that have recently engaged in trade wars using Tariffs? ________________      and ______________

8

Match the following definitions with the 3 Philosophical Principles of Ethics   Write A,B or C) :                                                (A) Imperative Principle;    (B) Generalization Argument;     (C) Utilitarian Principle:        _______Do what is right but filter action by considering consequences.                                           _______Do What is Right        ________Do what produces the Greatest Result.

9 Match 2 of the following with either:   (A)   INTEGRITY   or   (B) ETHICS (C) VALUES                                                                          _____Individual values pertaining to human behavior regarding What is Right or Wrong.        _____A person’s commitment and principles about honesty and sound moral character..

Consider the following data:

1. What is the regression equation? (Perform a Multiple Regression Analysis and Paste the table in the first answer box.)

2. State the hypotheses to test for the significance of the independent factors.

3. Which independent factors are significant at alpha= 0.05? Explain.

4. State the hypotheses to test for the significance of the regression equation. Is the regression equation significant at alpha=0.05? Explain.

5. How much of the variability in Y is explained by your model? Explain.

6. What tools would you use to check if the model has multicollinearity problems?

7. Does this model have multicollinearity problems? Explain.

8. If you were to propose a simplified model, eliminating some variables, what would it be? Why?

9. What tools would you use to check if the model assumptions are met?

10. Does this model meet the assumptions? Explain.

Python:

Lo Shu Magic Square

The Lo Shu Magic Square is a grid with 3 rows and 3 columns, shown in figures below. The Lo Shu Magic Square has the following properties:

The grid contains the numbers 1 through 9 exactly.

The sum of each row, each column, and each diagonal all add up to the same number. This is shown in Figure B.

In a program you can stimulate a magic square using a two-dimensional list. Write a function that accepts a two-dimensional list as an argument and determines whether the list is a Lo Shu Magic Square. Test the function in a program.

Figure A

Figure B

Exercise 3

The data in the table represent the "Exam Scores" for two random samples of students. The first group of = 6 students were under active-learning course, and the second group of = 6 students were under traditional lecturing. Note that the standard deviations in the Active group is = 3.43 and in the Traditional group is = 3.03.

Please answer the following questions underneath each question.

1. Which test is appropriate to compare the Exam-Scores in the two groups of students?

Answer:

2. Conduct the steps of this test

(please enumerate and write all the steps of your answer below)

Step 1:

3. State your conclusion in the context of this study

Exercise 3

The data in the table represent the "Exam Scores" for two random samples of students. The first group of n1 = 6 students were under active-learning course, and the second group of n2 = 6 students were under traditional lecturing. Note that the standard deviations in the Active group is s1= 3.43 and in the Traditional group is s2 = 3.03.

Please answer the following questions underneath each question.

1. Which test is appropriate to compare the Exam-Scores in the two groups of students?

Answer:

2. Conduct the steps of this test

(please enumerate and write all the steps of your answer below)

Step 1:

3. State your conclusion in the context of this study

Write a function add(vals1, vals2) that takes as inputs two lists of 0 or more numbers, vals1 and vals2, and that uses recursion to construct and return a new list in which each element is the sum of the corresponding elements of vals1 and vals2. You may assume that the two lists have the same length. For example: >>> add([1, 2, 3], [3, 5, 8]) result: [4, 7, 11] Note that: The first element of the result is the sum of the first elements of the original lists (1 + 3 –> 4). The second element of the result is the sum of the second elements of the original lists (2 + 5 –> 7). The third element of the result is the sum of the third elements of the original lists (3 + 8 –> 11).

Use recursion please / also please explain your codes for better understanding.

34. You own a​ firm, and you want to raise $40 million to fund an expansion.​ Currently, you own​ 100% of the​ firm's equity, and the firm has no debt. To raise the $40 million solely through​ equity, you will need to sell​ two-thirds of the firm. ​ However, you would prefer to maintain at least a​ 50% equity stake in the firm to retain control.
a. If you borrow $15 million, what fraction of the equity will you need to sell to raise the remaining $25 million? (Assume perfect capital​ markets.)
b. What is the smallest amount you can borrow to raise the $40 million without giving up​ control? (Assume perfect capital​ markets.)