I. Consider the random experiment of rolling a pair of dice. Note: Write ALL probabilities as reduced fractions or whole numbers (no decimals).

2) How many outcomes does the sample space contain? _____36________

3)Draw a circle (or shape) around each of the following events (like you would circle a word in a word search puzzle). Label each event in the sample space with the corresponding letter.

A: Roll a sum of 3.

B: Roll a sum of 6.

C: Roll a sum of at least 9.

D: Roll doubles.

E: Roll snake eyes (two 1’s). F: The first die is a 2.

3) Two events are mutually exclusive if they have no outcomes in common, so they cannot both occur at the same time.

Are C and F mutually exclusive? ___________

Using the sample space method (not a special rule), find the probability of rolling a sum of at least 9 and rolling a 2 on the first die on the same roll. P(C and F) = __________

Using the sample space method (not a special rule), find the probability of rolling a sum of at least 9 or rolling a 2 on the first die on the same roll.

P(C or F) = __________

4) Special case of Addition Rule: If A and B are mutually exclusive events, then

P(A or B) = P(A) + P(B)

Use this rule and your answers from page 1 to verify your last answer in #6:

P(C or F) = P(C) + P(F) = ________ + ________ = _________

5) Are D and F mutually exclusive? __________

Using the sample space method, P(D or F) = _________

6) Using the sample space method, find the probability of rolling doubles and rolling a “2” on the first die.

P (D and F) = _______

7) General case of Addition Rule: P(A or B) = P(A) + P(B) – P(A and B)

Use this rule and your answers from page 1 and #9 to verify your last answer in #8:

P(D or F) = P(D) + P(F) – P(D and F) = ________ + ________ − ________ = _________

8) Two events are independent if the occurrence of one does not influence the probability of the other occurring. In other words, A and B are independent if P(A|B) = P(A) or if P(B|A) = P(B).

Compare P(D|C) to P(D), using your answers from page 1: P(D|C) = ________ P(D) = ________ Are D and C independent? _________ because _______________________________

When a gambler rolls at least 9, is she more or less likely to roll doubles than usual? ___________ Compare P(D|F) to P(D), using your answers from page 1: P(D|F) = ________ P(D) = ________

Are D and F independent? __________ because ______________________________

9) Special case of Multiplication Rule: If A and B are independent, then P(A and B) = P(A) · P(B).

Use this rule and your answers from page 1 to verify your answer to #9: P(D and F) = P(D) • P(F) = ________ · ________ = ________ .

10) Find the probability of rolling a sum of at least 9 and getting doubles, using the sample space method.

P(C and D) = ___________ .

11) General case of Multiplication Rule: P(A and B) = P(A) · P(B|A).

Use this rule and your answers from page 1 to verify your answer to #13: P(C and D) = P(C) • P(D|C) = ________ · ________ = ________ .

Please answer form 6-14

I. Consider the random experiment of rolling a pair of dice. Note: Write ALL probabilities as reduced fractions or whole numbers (no decimals).

1) One possible outcome of this experiment is 5-2 (the first die comes up 5 and the second die comes up 2). Write out the rest of the sample space for this experiment below by completing the pattern:

2) How many outcomes does the sample space contain? _____________

3) Draw a circle (or shape) around each of the following events (like you would to circle a word in a word search puzzle). Label each event in the sample space with the corresponding letter. Event A has been done for you.

A: Roll a sum of 3.
B: Roll a sum of 7.
C: Roll a sum of at least 10.

D: Roll doubles.
E: Roll snake eyes (two 1’s). F: First die is a 4.

4) Find the following probabilities:
P(A) = _________ P(B) = _________ P(C) = _________

P(D) = _________ P(E) = _________ P(F) = _________

5) The conditional probability of B given A, denoted by P(B|A), is the probability that B will occur when A has already occurred. Use the sample space above (not a special rule) to find the following conditional probabilities:

P(D|C) = _________ P(E|D) = _________ P(D|E) = _________ P(A|B) = _________ P(C|F) = _________

6) Two events are mutually exclusive if they have no outcomes in common, so they cannot both occur at the same time.

Are C and E mutually exclusive? ___________
Find the probability of rolling a sum of at least 10 and snake eyes on the same roll, using the

sample space (not a special rule).
P(C and E) = __________

Find the probability of rolling a sum of at least 10 or snake eyes, using the sample space. P(C or E) = __________

7) Special case of Addition Rule: If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Use this rule to verify your last answer in #6:
P(C or E) = P(C) + P(E) = ________ + ________ = _________

8) Are C and F mutually exclusive? __________ Using sample space, P(C or F) = _________ 9) Find the probability of rolling a “4” on the first die and getting a sum of 10 or more, using the

sample space.
P (C and F) = ________

10) General case of Addition Rule: P(A or B) = P(A) + P(B) – P(A and B) Use this rule to verify your last answer in #8:

P(C or F) = P(C) + P(F) – P(C and F) = ________ + ________ − ________ = _________

11) Two events are independent if the occurrence of one does not influence the probability of the other occurring. In other words, A and B are independent if P(A|B) = P(A) or if P(B|A) = P(B).

Compare P(D|C) to P(D), using the sample space: P(D|C) = ________ . P(D) = ________ .
Are D and C independent? _________
When a gambler rolls at least 10, is she more or less likely to roll doubles than usual? ___________ Compare P(C|F) to P(C), using the sample space: P(C|F) = ________ . P(C) = ________ .

Are C and F independent? __________
12) Special case of Multiplication Rule: If A and B are independent, then P(A and B) = P(A) · P(B).

Use this rule to verify your answer to #9:
P(C and F) = P(C) • P(F) = ________ · ________ = ________ .

13) Find the probability of rolling a sum of at least 10 and getting doubles, using the sample space. P(C and D) = ________ .

14) General case of Multiplication Rule: P(A and B) = P(A) · P(B|A). Use this rule to verify your answer to #13:

P(C and D) = P(C) • P(D|C) = ________ · ________ = ________ .

3. Ecological Categories Insect activity at a dead body can be divided into four major categories matching the ecological role they play. Some insects are attracted to a dead body and use the body as a source of food. Other insects are attracted to a dead body to feed on the first group, the insects that are using the body for food. "It's a bug-eat-bug-word, out there!" And some insects are attracted to a dead body to use as an extension of their habitat. Below are examples of each. (The links included direct you to optional BugGuide pages where you can read more about the insect groups.) 1. Necrophagous species: (the word necrophagous is from nekros, from the Greek meaning dead, and phagein, meaning to devour). Necrophagous insects feed on the body and are the most important species in establishing time of death because insects that find and use a dead body as a source of food arrive in a predictable sequence based on the state of decomposition of the body. These insects are referred to as indicator species. Examples: o Blow flies (Diptera: Calliphoridae) are metallic blue or green flies slightly larger than a house fly. They are also known as bottle flies. They are attracted to the odors of decay and may find a dead body within hours. The female fly deposits masses of eggs around body openings and the eggs hatch within 24 hours. The larvae feed on dead animal tissue though at times are found dung, and similar materials. When fully grown the larvae pupate on the body or in the soil under and around the body. Newly emerged adult flies will not return to the body to lay more eggs. o Flesh flies (Diptera: Sarcophagidae) are medium-sized and resemble the blow flies and house flies. Flesh flies are dull colored with black and gray stripes on the thorax and checkering on the abdomen. The flesh flies show up on a dead body slightly later than the blow flies. Flesh flies do not lay eggs. Instead the females deposit first instar larvae that were hatched internally, directly on the body. o House flies (Diptera: Muscidae) do not show up until the body is in advanced stages of decomposition. o Carrion or burying beetle (Coleoptera: Silphidae) adults may feed on decaying animal tissue, though their larvae feed on the fly maggots feeding on dead animals. They are therefore slight later to arrive on the scene than are the flies. o The larvae of carpet beetles and larder beetles (Coleoptera: Dermestidae) feed on dried organic material, including carrion. 2. Predators and parasites of the necrophagous species mentioned above are the second most important group in forensic entomology. These arrive after the first wave is wellestablished. Examples: o The larvae and adults of burying beetles (already mentioned) consume flesh, but also eat fly larvae found in the carcass. o Rove beetles (Coleoptera: Staphylinidae) prey on maggots that are feeding within carrion. 3. Omnivorous species: wasps, ants, and some beetles feed both on the corpse and its inhabitants 4. Adventive species: use the corpse as an extension of their environment, that is, primarily a place to hide. o Collembola- springtails o Spiders In some situations, based upon an understanding of the life cycle, habits and biology of these carrion-associated insects, the presence of particular species can provide not only clues to the time of death, but also to the general location of death (e.g. city vs. rural areas) and possibly whether the person died inside a building or outdoors. These clues are based upon the biological and ecological characteristics of a particular species; their life cycles, and seasonal and geographical occurrence.

The rate of development (that is, growth) of blow fly and flesh fly larvae is variable but predictable, which allows them to be used to estimate time since death. How are the age of maggots collected by a forensic entomologist at the scene, the surrounding environmental conditions, and the postmortem interval connected? This is supposed to be an easy question, even if awkwardly worded. Don't make it harder than it is. What external factor determines how quickly or slowly a maggot grows and therefore the age and the size of collected maggots?

•• P11.1 Phone numbers and PIN codes can be easier to remember when you find words that
spell out the number on a standard phone keypad. For example, instead of remembering
the combination 2633, you can just think of CODE.
Write a recursive function that, given a number, yields all possible spellings (which
may or may not be real words).
•• P11.2 Continue Exercise P11.1, checking the words against the /usr/share/dict/words file on
your computer, or the words.txt file in the companion code for this book. For a given
number, return only actual words.
••• P11.3 With a longer number, you may need more than one word to remember it on a
phone pad. For example, 846-386-2633 is TIME TO CODE. Using your work from
Exercise P11.2, write a program that, given any number, lists all word sequences that
spell the number on a phone pad.
••• P11.4 Change the permutations function of Section 11.4 (which computed all permutations
at once) to a PermutationIterator (which computes them one at a time).
class PermutationIterator
{
public:
PermutationIterator(string s) { . . . }
string next_permutation() { . . . }
bool has_more_permutations() { . . . }
};
Here is how you would print out all permutations of the string "eat":
PermutationIterator iter("eat");
while (iter.has_more_permutations())
{
cout << iter.next_permutation() << endl;
}
Now we need a way to iterate through the permutations recursively. Consider the
string "eat". As before, we’ll generate all permutations that start with the letter 'e',

then those that start with 'a', and finally those that start with 't'. How do we generate
the permutations that start with 'e'? Make another PermutationIterator object
(called tail_iterator) that iterates through the permutations of the substring "at". In
the next_permutation function, simply ask tail_iterator what its next permutation is,
and then add the 'e' at the front. However, there is one special case. When the tail
iterator runs out of permutations, all permutations that start with the current letter
have been enumerated. Then
• Increment the current position.
• Compute the tail string that contains all letters except for the current one.
• Make a new permutation iterator for the tail string.
You are done when the current position has reached the end of the string.
••• P11.5 The following program generates all permutations of the numbers 0, 1, 2, ... , n – 1,
without using recursion.
#include <iostream>
#include <vector>
using namespace std;
void swap(int& x, int& y)
{
int temp = x;
x = y;
y = temp;
}
void reverse(vector<int>& a, int i, int j)
{
while (i < j)
{
swap(a[i], a[j]); i++; j--;
}
}
bool next_permutation(vector<int>& a)
{
for (int i = a.size() - 1; i > 0; i--)
{
if (a[i - 1] < a[i])
{
int j = a.size() - 1;
while (a[i - 1] > a[j]) { j--; }
swap(a[i - 1], a[j]);
reverse(a, i, a.size() - 1);
return true;
}
}
return false;
}
void print(const vector<int>& a)
{
for (int i = 0; i < a.size(); i++)
{
cout << a[i] << " ";
}
cout << endl;

}
int main()
{
const int n = 4;
vector<int> a(n);
for (int i = 0; i < a.size(); i++) { a[i] = i; }
print(a);
while (next_permutation(a)) { print(a); }
return 0;
}
The algorithm uses the fact that the set to be permuted consists of distinct numbers.
Thus, you cannot use the same algorithm to compute the permutations of the
characters in a string. You can, however, use this technique to get all permutations of
the character positions and then compute a string whose ith character
is s[a[i]]. Use
this approach to reimplement the generate_permutations function without recursion.
•• P11.6 Refine the is_palindrome function to work with arbitrary strings, by ignoring nonletter
characters and the distinction between upper- and lowercase letters. For
example, if the input string is
"Madam, I’m Adam!"
then you’d first strip off the last character because it isn’t a letter, and recursively
check whether the shorter string
"Madam, I’m Adam"
is a palindrome.

Question: Properly convert the solution to this problem from Java to C++

Problem Statement

If you want to write a message anonymously, one way to do it is to cut out letters from headlines in a newspaper and paste them onto a blank piece of paper to form the message you want to write. Given several headlines that you have cut out, determine how many messages from a list you can write using the letters from the headlines. You should only consider each message by itself and not in conjunction with the others, see example 2.

Write the function how_many which takes as parameters a vector<string> headlines containing the headlines which you have cut out as well as a vector<string> messages with the messages you may want to write, and returns an int which is the total number of messages you can write.

Constraints

• All letters that you cut out can be used both as upper or lower case in a message.
• Spaces should be ignored in elements in both headlines and messages.
• headlines will contain between 1 and 50 elements, inclusive.
• messages will contain between 1 and 50 elements, inclusive.
• The length of each element in headlines will be between 1 and 50 characters, inclusive.
• The length of each element in messages will be between 1 and 50 characters, inclusive.
• Each element in headlines will only contain the letters 'A'-'Z', 'a'-'z' and space.
• Each element in messages will only contain the letters 'A'-'Z', 'a'-'z' and space.

Examples

1. headlines =
   
   {"Earthquake in San Francisco",
    "Burglary at musuem in Sweden",
    "Poverty"}
   
   messages =
   
   {"Give me my money back",
    "I am the best coder",
    "TOPCODER"}
   
   Returns: 2
   

   In the first message we have three 'm's, but there are only two 'm's among the headlines (both in the word "museum"), so this message can't be written.

   The second message can be written. Note that the first letter, 'I', only appears as lower case in the headlines, but that's allowed. The last message can also be written, so the method should return 2.

2. headlines = 
   
           {"Programming is fun"}
   
   messages = 
   
           {"program","programmer","gaming","sing","NO FUN"}
   
   Returns: 4
   

   The messages "program", "gaming", "sing" and "NO FUN" can all be written but not "programmer" (no 'e's exist). The method should return 4.

3. headlines = 
   
      {"abcdef","abcdef"}
   
   messages = 
   
      {"AaBbCc","aabbbcc","   ","FADE"}
   
   Returns: 3
   

   All messages except the second one can be written, because it contains three 'b's but there are only two 'b's available. Also note the message only containing spaces - such a message can of course always be written.

Given Function

#include <vector>
#include <string>

int how_many(vector<string> headlines, vector<string> messages) {
// fill in code here
}

Solution (Convert the Java code below to C++).

import java.util.*;

public class Anonymous {
      public int howMany(String[] headlines, String[] messages) {
          
    
          HashMap<Character, Integer> lettersAvailable = countLetters(headlines);

          int wordsWeCanMake = 0; 
          for(String message : messages){
                  String[] oneMessage = {message}; 
                  HashMap<Character, Integer> lettersNeeded = countLetters(oneMessage);
                  boolean canMakeMessage = true;
                  Iterator it = lettersNeeded.entrySet().iterator(); 
                  while (it.hasNext()){
                          Map.Entry pairs = (Map.Entry)it.next();
                          char key = (Character) pairs.getKey(); 
                          if(!(key==' ')){
                                  int numNeeded = (Integer) pairs.getValue();
                                  if(lettersAvailable.containsKey(key)){
                                          int numAvailable = lettersAvailable.get(key); 
                                          canMakeMessage = (numNeeded <= numAvailable) && canMakeMessage;
                                  }
                                  else{
                                          canMakeMessage = false ; 
                                          break;
                                  }
                          }
                          
                      it.remove();
                  }
                  if(canMakeMessage){
                          wordsWeCanMake += 1; 
                  }
          }
          return wordsWeCanMake; 
      }
      
      public HashMap<Character, Integer> countLetters(String[] words){
          HashMap<Character, Integer> counts = new HashMap<Character, Integer>();
          int currentCountOfLetter = 0;
          
          for(String word : words){  
                  for(int i=0; i<word.length(); i++){
                          char letter = Character.toLowerCase(word.charAt(i));
                          if (counts.containsKey(letter)){
                                  currentCountOfLetter = counts.get(letter);
                                  currentCountOfLetter +=1; 
                          }
                          else {
                                  currentCountOfLetter = 1;
                          }
                          counts.put(letter, currentCountOfLetter); 
                  }
          }
          
          return counts; 
      }
      }
}

Critical Thinking

The market for young people's food products has increased considerably in recent years. As a result, children have become high-potential customers and are now the focus of intense and specialized marketing and advertising efforts.

Children and adolescents have become attractive consumers and influencers: they have an increasing influence on their family's purchases.Childrenrepresent an important target audience for marketers because they have their own purchasing power, influence their parents' purchasing decisions, and are the consumers of tomorrow. Advertisers have an interest in seducing them from an early age.Thus, to be sure to attract young people, companies opt for a combination of different approaches and channels such as television advertising, contests and games, toys, the use of popular characters, the use of various attractive colors, school marketing, Internet and branded products etc.

Food and beverages products that target children have increased and these productsare dominated by foods that are high in calories, sugars, salt, fat, low in nutrients and therefore not compatible with national dietary recommendations.

Mr. Fahmy has already a business in the food sector and wants to open a new subsidiary specializing in natural and organic products for children. The goal is to provide healthy, nutritious food and use healthier ingredients.

Questions

1. Help Mr. Fahmy define his overall goals, objectives and strategies for his new business in the context of his mission and purpose.

2. Briefly describe the choices that Mr. Fahmy can make for each of the 4 Ps of the marketing mix.

3. Identify the target market and describe how Mr. Fahmy's activities will respond better than the competition to the needs of the consumer. (List consumer expectations for the product)

4. Describe the type of promotional methods that you recommend to Mr. Fahmy for the promotion of his product line. (Identify techniques such as word of mouth, personal sales, direct marketing, sales promotion, etc., on television, radio, social media, and newspapers).

5. Why is it important for a media planner to consider how different types of media could work together on a media plan?

Two different machines, A and B, used for torsion tests of steel wire were tested on 12 pairs of different types of wire, with one member of each pair tested on each machine.

The results (break angle measurements) were as follows:

Machine A: 32, 35, 38, 28, 40, 42, 36, 29, 33, 37, 22, 42

Machine B: 30, 34, 39, 26, 37, 42, 35, 30, 30, 32, 20, 41

[a] Construct a side-by-side boxplot to display the two data sets and comment on interesting features.                                                                                                                                                                  [4 pt]

[b] Construct a QQ-plot (with a qqline) for each data set.                                                                 [3 pt]

How would you describe your Q-Q plot?

[c] Perform a Shapiro-Wilks normality test on each data set. What are the results regarding the data sets?                                                                                                                                                                        [3 pt]

[d] Based on your results [a] through [c], can you conduct a two-sample t-test for the data sets? Explain your response.                                                                                                             

Answer:           Yes                  No                   E Circle one                                                              [1 pt]

Explanation:                                                                                                                                       [3 pt]

[e] Is there evidence at the 5% significance level to suggest that machines A and B give different mean readings?

Write the null and alternative hypotheses test symbolically and verbally.                                        [8 pt]

Use R to get analysis results. State what the results tell you about the data.                                     [8 pt]

[f] Is there evidence at the 5% significance level to suggest that machine B gives a lower average reading than machine A?

Write the null and alternative hypotheses test symbolically and verbally.                                        [8 pt]

Use R to get analysis results. State what the results tell you about the data.                                     [8 pt]

[g] Your R codes or Excel commands for parts [a], [b], [c], [e], and [f] are required for credit.      [10 pt]

Copy and paste them here or paste them onto a blank MS Word document.

1. For the data below create a table in excel and a graph to accompany. (the table and graph are two separate supplements so make sure each is labeled and formatted properly.) Hint: You are making the table in excel because you can make the graph straight from the data.

Each group recorded the level of carbon monoxide measured (ppm) in a running car every 15 seconds for 2 minutes with a Graywolf indoor/outdoor air quality monitor. They start recording at zero seconds.

Group 1, 1994 Ford Focus: 58, 50, 42, 36, 30, 25, 25, 24, 23

Group 2, 2008 Ford F150: 12, 15, 15, 16, 17, 16, 15, 14, 15

Group 3, 1988 Chevy Nova: 112, 80, 80, 70, 60, 55, 45, 40, 40

Group 4, 2014 Honda Accord: 12, 14, 16, 20, 30, 30, 35, 40, 48

Group 5, 2010 Hyundai Santa Fe: 50, 45, 43, 42, 30, 23, 13, 8, 7

Group 6, 2003 Subaru Forester: 66, 45, 40, 33, 32, 21, 20, 120, 17

2. Create a table in Microsoft word for the following data.

Scientists tracked and observed a Black Bear (Ursus Americanus) named Stachi over the course of 6 years. Once a year they would document her weight and height, geolocation, fetal development, and body condition.

December 1999- 97 lbs., 55 in., (39.7576202, -74.1062466), No, Average

December 2000- 135 lbs., 55 in., (39.695866, -74.253511), Yes, Fat

December 2001- 102 lbs., 55 in., (39.5585, -74.3706), No, Average

December 2002- 99 lbs., 55 in., (39.7576202, -74.1062466), No, Average

December 2003- 122 lbs, 55 in., (39.695866, -74.253511) Yes, Fat

December 2004- 70 lbs., 54 in., (39.49026, -74.53915), No, Thin

Abc Corporation was incorporated on December 1, 2019 and had following transactions during December

1 Dec Issued Capital for 5000 cash

 3 Dec Paid 1200 cash for three months rent in advance

 4 Dec Purchased a used truck for 10,000 on credit

 4 Dec Purchased Supplies of 1000 on credit

 6 Dec Paid 1800 for a one-year truck insurance policy

 7 Dec Billed a customer 4500 for work completed to date

 8 Dec Collected 800 for work completed to date

 12 Dec Paid the following expense in cash

 Advertisement 350

 Interest 100

 Telephone 75

 truck operating 425

 Wages 2500 

15 Dec Collected 2000 of the amount billed on 7 dec

 18 Dec Billed Customer 6500 for work completed to date

 19 Dec Signed a 9000 contract for work to be performed in Jan 2017

 22 Dec Paid the following Expenses

 Advertisement 200

 Interest 150

 Truck Operating 375

 Wages 2500

 27 Dec Collected advance on work to be done in January

 28 Dec Received a bill for 100 for electricity used during the month

Additional Information The following information relates t0 31 Dec , 2016 One month of the prepaid insurance has expired The December portion of the rent paid is expired A physical count indicates that 350 of supplies is still on hand The amount collected as advance is unearned Three days of wages for Dec 29 30 31 are unpaid: Unpaid amount of 1500 will be included in first wages payment in Jan The truck has an estimated useful life of 4 years Income tax expenses are 500. The amount is to be paid next year.

Required:

Prepare trasaction summary,general journal, entries to ledger account, trial balance,adjusted trial balnce, financial statemment(income statement,owners equity,balance sheet), close temporary accounts and worksheet.

Intructions: should be handwritten or word file depend on you