My sons (“Boy 1” and “Boy 2”) are negotiating over how to divide a pile of 20 chocolates. Boy 1 will engage Boy 2 in up to three rounds of negotiations. The order of events is:

FIRST ROUND: Boy 1 makes Boy 2 an initial offer. Boy 2 accepts or rejects. If he accepts, the game ends and the two boys get their chocolates. If Boy 2 rejects, I punish them for not working together by eating 5 chocolates myself. The game then continues with 15 chocolates to be divided.

SECOND ROUND: Boy 2 makes an offer. Boy 1 accepts or rejects. If he accepts, the game ends and the two boys get their chocolates. If Boy 1 rejects, I eat 5 chocolates myself and the game continues with 10 chocolates to be divided.

THIRD ROUND: Boy 1 makes a final offer. Boy 2 accepts or rejects. If he accepts, the two boys get their chocolates. If Boy 2 rejects, the game ends and I eat all the remaining chocolates. Note that I am expecting you to make an assumption of spiteful players, all else equal. Said another way, I assume that “reject” will break the indifference of getting zero either way...

(a) (5) If we reach the third round of the game, what would be Boy 1’s offer?

(b) (5) Given that my sons know (a) in round 2, what would be Boy 2’s 2nd Round offer?

(c) (5) Given that my sons know (b) in round 1, what would be Boy 1’s 1st Round offer?

(d) (10) What is Boy 1’s first-round strategy? What is Boy 2’s first-round strategy? What is the equilibrium outcome of the game?

2. (25) My sons (“Boy 1” and “Boy 2”) are negotiating over how to divide a pile of 20 chocolates. Boy 1 will engage Boy 2 in up to three rounds of negotiations. The order of events is:

FIRST ROUND: Boy 1 makes Boy 2 an initial offer. Boy 2 accepts or rejects. If he accepts, the game ends and the two boys get their chocolates. If Boy 2 rejects, I punish them for not working together by eating 5 chocolates myself. The game then continues with 15 chocolates to be divided.

SECOND ROUND: Boy 2 makes an offer. Boy 1 accepts or rejects. If he accepts, the game ends and the two boys get their chocolates. If Boy 1 rejects, I eat 5 chocolates myself and the game continues with 10 chocolates to be divided.

THIRD ROUND: Boy 1 makes a final offer. Boy 2 accepts or rejects. If he accepts, the two boys get their chocolates. If Boy 2 rejects, the game ends and I eat all the remaining chocolates. Note that I am expecting you to make an assumption of spiteful players, all else equal. Said another way, I assume that “reject” will break the indifference of getting zero either way...

(a) (5) If we reach the third round of the game, what would be Boy 1’s offer?

(b) (5) Given that my sons know (a) in round 2, what would be Boy 2’s 2nd Round offer?

(c) (5) Given that my sons know (b) in round 1, what would be Boy 1’s 1st Round offer?

(d) (10) What is Boy 1’s first-round strategy? What is Boy 2’s first-round strategy? What is the equilibrium outcome of the game?

1. An oil tanker belonging to Oil Finders, Inc. runs aground and causes a massive oil spill that damages several miles of the Texas coastline. As a result, several public beaches are rendered unusable to the public. Riker and Picard are avid surfers who like to hit the waves as often as they can. Because of the oil spill, they will not be able to surf for at least six months. They file suit against Oil Finders, Inc. for nuisance. Will the court hear their suit? Defend your answer.

2. An oil tanker belonging to Oil Finders, Inc. runs aground and causes a massive oil spill that damages several miles of the Texas coastline. As a result, several public beaches are rendered unusable to the public. Riker and Picard make their living harvesting clams and oysters at the various beaches in the area and their business has been destroyed as a result of the oil spill. They file suit against Oil Finders, Inc. for nuisance. Will the court hear their suit? Defend your answer.

3.John and Kelsey live in a house in Missouri that they purchased for $250,000. The town has never had a garbage dump and the city government has spent millions of dollars over the years sending the town's trash to a dump located in a different part of the state. In order to save money, the town contracts with Mr. Barr, the president of a waste management company, to build and maintain a landfill at the edge of the town. Within six months, the landfill is operational. Eventually, as more and more of the town's trash gets dumped into the landfill, the residents of the town are subjected to the odor that the landfill gives off. The odor is not constant but, on windy days, it is noticeable. As a result, the house that John and Kelsey bought for $250,000 is reduced in value to $240,000. If John sues the town for nuisance, which of the following is most likely to occur?

Defend your answer/ Win, because his house's value has been reduced.

Win, because John moved to the neighborhood before the landfill opened.

Lose, because the odor is not constant. Lose, because benefits of the landfill outweigh the damage done to John.

7. You are a small farmer in a poor Latin American country. You are trying to decide whether to continue to cultivate a traditional strain of wheat or switch to a new high-yield variety. If you plant the traditional strain, the yield of your wheat field (X) is approximately normally distributed with mean 70 bushels and standard deviation 6 bushels. If you plant the high-yield variety, the yield of your wheat field (Y) is approximately normally distributed with mean 80 bushels and standard deviation 12 bushels. Your family requires 65 bushels of wheat. Let’s assess the relative riskiness of the traditional strain and the high-yield variety.

a. If you grow the traditional variety of wheat, the probability that the yield will be less than 65 bushels is ____.  FOUR DECIMALS.

b. If you grow the high-yield variety of wheat, the probability that the yield will be less than 65 bushels is ______ .  FOUR DECIMALS.

In addition to wheat, you also grow bananas. Your banana yield (W) is approximately normally distributed with mean 100 bushels and standard deviation 4 bushels. If you grow the traditional variety of wheat, your wheat yield and banana yield have a correlation of 0.5. However, if you grow the high-yield variety, your wheat yield and banana yield have a correlation of – 0.5 (a negative correlation). You sell all bananas (your family does not need any bananas), plus any wheat in excess of the 65 bushels for your family. The market price of wheat is $2 per bushel and the market price of bananas is $4 per bushel (in other words, you get $2 per bushel for the wheat and $4 per bushel for the bananas you sell). You need to earn $400 to pay the landlord rent on your farm. Let’s compare the probabilities that you’ll earn at least enough income to pay your rent.

c. The covariance between X and W is ________ . The covariance between Y and W is _______ .  INTEGERS (NO DECIMALS).

d. Use R to represent income from selling wheat and bananas. R as a function of X and W is R=  . R as a function of Y and W is R= ______ .  EQUATIONS, NO SPACES.

e. If you grow the traditional variety of wheat, your expected income (R) is_________ and the variance of income is _____________.  INTEGERS (NO DECIMALS).

f. If you grow the high-yield variety of wheat, your expected income (R) is_________ and the variance of income is ___________ .  INTEGERS (NO DECIMALS).

g. If you grow the traditional variety of wheat, the probability that your income will be at least $400 is __________.  FOUR DECIMALS.

h. If you grow the high-yield variety of wheat, the probability that your income will be at least $400 is ___________ .  FOUR DECIMALS.

IN C++

Note: While there are many ways to do conversions to pig latin, I will require that you follow the procedures below, all of which will use the following structure:

struct Word {
 string english;
 string piglatin;
};

Part 1. Write a function that takes in an English sentence as one string. This function should first calculate how many “words” are in the sentence (words being substrings separated by whitespace). It should then allocate a dynamic array of size equal to the number of words. The array contains Word structures (i.e. array of type Word). The function would then store each word of that sentence to the english field of the corresponding structure. The function should then return this array to the calling function using the return statement, along with the array size using a reference parameter.

This function should also remove all capitalization and special characters other than letters. Implement the function with the following prototype

Word * splitSentence(const string words, int &size);

Part 2. Write a function that takes in an array of Word structures and the size of the array and converts each english field to the corresponding piglatin field.

void convertToPigLatin(Word [] wordArr, int size);

To do this conversion, if a word starts with a consonant, the piglatin conversion of the word involves moving the first letter of the word to the end of the string and then adding “ay” to the end.

pig -> igpay

cat -> atcay

dog -> ogday

If the word starts with a vowel, simply add “way” to the end of the word

apple -> appleway

are -> areway

Part 3. Write a function that takes in an array of Word structures and outputs the pig latin part of it to the screen, with each word separated by a space.

void displayPigLatin(const Word [] wordArr, int size);

Example:

Please enter a string to convert to PigLatin:
Casino is nothing but a Goodfellas knockoff
Output:
asinocay isway othingnay utbay away oodfellasgay nockoffkay 

Error conditions: Your program should get rid of all punctuation and special characters other than letters. Your program should be able to deal with there being two or more spaces between words.

Note: Make sure to follow proper programming style, as per the style supplement.

Reflective Question # 1:
Venezuela is a Latin American country that is rich in oil preserves. This petroleum sector is
mainly owned by the government, in a sense that it controls and prices it. The petroleum sector
constitutes around 85% of the exports in the country. In Venezuela, there are very few private
sectors.
Germany is one of the top 5 richest countries in the world. It provides its citizens varieties in
consumer goods and business services. But the government imposes regulations even in those
areas to protect its citizens. Thus, the decision about what to produce is distributed among
private and public sectors.
1- What type of economic systems do Venezuela and Germany apply? Explain.
2- For a certain country to adopt a market economic system, what are the decisions they need to
take? Illustrate by providing an example.

1). If a couple has two children, what is the probability that they are both girls assuming that the older one is a girl?

2). Suppose that we have two dice, the first one being a regular die, and the second weighted so that half the time it rolls a 1, and half the time it rolls a 2 (it never rolls anything else). If we choose one of these dice at random, and roll a 1, what’s the probability that it is the regular die?

1f. Compare 1a and 1d, and 1b and 1e, explain why the percentage in 1a is much larger than that in 1d and why the value in 1b is much smaller than that in 1e?

1. Suppose that for Edwardsville High School, distances between students’ homes and the high school observe normal distribution with the average distance being 4.76 miles and the standard deviation being 1.74 miles. Express distances and z scores to two decimal places. Write the formula to be used before each calculation.

1a. What percentage of students in the high school live farther than 6.78 miles from the school?

1b. A survey shows that 8% of the students who live closest to the school choose to walk to school. What is the maximum walking distance of these 8% of students? In other words, what is the distance below which these 8% of students live from the school?

1c. Suppose that the school district’s policy allows students living beyond 4.50 miles from the school to take school buses to go to school. There are 3,567 students who enroll in the fall semester, 2006. How many students in the high school are not eligible to take school buses?

1d. Suppose all samples of size 12 are taken. What percentage of sample means has a value larger than 6.78 miles?

1e. Below what value are 8% of sample means of size 12?

IN MINITAB  High School Dropouts Approximately 10.3% of American high school students drop out of school before graduation. Choose 10 students entering high school at random. Find the probability that

a. No more than two drop out

b. At least 6 graduate

c. All 10 stay in school and graduate