Mean: 16.07 SD: 0.89

Add graphs for all probabilities below questions. Include them in the file upload for Part 1. Include parameter labels and the shaded areas labeled.

1. Find the probability that a state's living wage is more than the minimum wage of $7.25 per hour. (round to 4 decimal places).

2. Find the probability of a state's living wage being more than the poverty level of $10.60 per hour. (round to 4 decimal places).

3. We wanted to ensure that 80% of families are earning a living wage, so we need to determine what the new minimum wage should be. The corresponding wage for 80% of families earning a living wage is: $ per hour (round to 2 decimals).

4. The z-score is: (round to 2 decimals).

1. (complete chart) Bank of America sells a 12 year fixed rate bond at 6%. At the same time of the issue the company buys a receiver swaption, 6% and paying variable rate based on LIBOR with 5 years remaining to expiration, 2.5% premium. Fill in the table below assuming the exercise of the swaption - complete bond

2. Explain the net effect to BOA

3. Explain the net effect to bondholders

please write legible

(House Selling Price) The data below show the selling price, square footage, bedrooms, and age of houses that have sold in a neighborhood in the last six months. Selling price Square footage Bedrooms Age 64,000 1,670 2 30 59,000 1,339 2 25 61,500 1,712 3 30 79,000 1,840 3 40 87,500 2,300 3 18 92,500 2,234 3 30 95,000 2,311 3 19 113,000 2,377 3 7 115,000 2,736 4 10 138,000 2,500 3 1 142,500 2,500 4 3 144,000 2,479 3 3 145,000 2,400 3 1 147,500 3,124 4 0 144,000 2,500 3 2 155,500 4,062 4 10 165,000 2,854 3 3 Develop seven regression models as below using the corresponding Excel data. ( Model 1) Y = selling price, X 1 = square footage (House Selling Price Model 1 Data) ( Model 2) Y = selling price, X2 = bedrooms (House Selling Price Model 2 Data) ( Model 3) Y = selling price, X3 = age (House Selling Price Model 3 Data) ( Model 4) Y = selling price, X 1 = square footage, X2 = bedrooms (House Selling Price Model 4 Data) ( Model 5) Y = selling price, X 1 = square footage, X3 = age (House Selling Price Model 5 Data) ( Model 6) Y = selling price, X2 = bedrooms, X3 = age (House Selling Price Model 6 Data) ( Model 7) Y = selling price, X 1 = square footage, X2 = bedrooms, X3 = age (House Selling Price Model 7 Data) (House Selling Price) Models 4, 5, and 6 are multiple regression models with two independent variables. Model 7 is a multiple regression model with three independent variables. (a) The adjusted r2 value of model 4 is ___. [Answer format: one decimal place] (b) The adjusted r2 value of model 5 is ___. [Answer format: two decimal places] (c) The adjusted r2 value of model 6 is ___. [Answer format: one decimal place] (d) The adjusted r2 value of model 7 is ___. [Answer format: two decimal places] Write your answer(s) as 1.2, 3.45, 6.7, 8.91

Prove via induction the following properties of Pascal’s Triangle:

•P(n,2)=(n(n-1))/2

• P(n+m+1,n) = P(n+m,n)+P(n+m−1,n−1)+P(n+m−2,n−2)+···+P(m,0) for all m ≥ 0

Web Mining Assignments

Exercise 6.1.1 : Suppose there are 100 items, numbered 1 to 100, and also 100 baskets, also numbered 1 to 100. Item i is in basket b if and only if i divides b with no remainder. Thus, item 1 is in all the baskets, item 2 is in all fifty of the even-numbered baskets, and so on. Basket 12 consists of items {1, 2, 3, 4, 6, 12}, since these are all the integers that divide 12. Answer the following questions:

(a) If the support threshold is 5, which items are frequent?
! (b) If the support threshold is 5, which pairs of items are frequent?

! (c) What is the sum of the sizes of all the baskets?

PS： I know the answer of a) which are 1, 2, 3, 4 ... 18, 19, 20. But how to get the answers of b) and c) please show the steps and the explanation. Thank you.

Prove the following using the method suggested:
(a) Prove the following either by direct proof or by contraposition:
Let a ∈ Z, if a ≡ 3 (mod 5) and b ≡ 2 (mod 5), then ab ≡ 1 (mod 5).

(b) Prove the following by contradiction:
Suppose a, b ∈ Z. If a² + b²
is odd, then (2|a) ⊕ (2|b), where ⊕ is the exclusive disjuntion,
i.e. p ⊕ q = (p ∨ q) ∧ ¬(p ∧ q).

(d) Prove the following by cases: For all n ∈ Z, n
2 + 3(n + 1) is odd.

(e) Prove the following by induction:
For n ≥ 1,
1 × 2 + 2 × 3 + 3 × 4 + · · · + n(n + 1) = n/3
(n + 1)(n + 2)

Let X ∈{1,2} and Y ∈{3,4} be independent random variables with PMF-s: fX(1) = 1 2 fX(2) = 1 2 fY (3) = 1 3 fY (4) = 2 3 Answer the following questions (a) Write down the joint PMF

(b) Calculate P(X + Y 6 5) and P(Y −X > 2)

(c) Calculate E(XY ), E(X2Y ), E(︁X2+1 Y−2)︁

(d) Calculate the Cov(X,Y ), Cov(1−X,3Y + 2) and Var(2X −Y ) (

e*) Calculate Cov(XY,X), Cov(XY,X + Y ) and Var(︀X Y)︀

I have one error and it encounters my split array and it should output true or false

public class Main
{

private static int[] freq;

static boolean doubleOrNothing(int[] array, int size, int i)
{
  
if (size <= 1)
  
return false;

if (2 * array[i] == array[i+1])

return true;

return doubleOrNothing(array, size - 1, i++);
}

/**
*
* @param word
* @param sep
*
*
* @param count
* @return
*/
public static String wordSeparator(String word, String sep, int count)
{
  
if (count <= 0)
  
return "";
  
String new_word="";
if (count == 1)
return word;

return word + sep + wordSeparator(word, sep, count - 1);
  
}
static boolean mcNuggetNumber(int n) //checks for 3 or 7 piece chicken nugget
{
boolean l = false, r = false;
if (n == 3 || n == 7)
return true;
  
if (n >= 3)
l = mcNuggetNumber(n - 3);
  
if (n >= 7)
r = mcNuggetNumber(n - 7);
  
return l || r;
  
}

static boolean splitArray(int arr[], int n, int k)
{
// An odd length array cannot be divided into pairs
if (n == 1)
return false;

// Create a frequency array to count occurrences
// of all remainders when divided by k.
// map freq = null;

// Count occurrences of all remainders
for (int i = 0; i < n; i++)
freq[arr[i] % k]++;

// Traverse input array and use freq[] to decide
// if given array can be divided in pairs
for (int i = 0; i < n; i++)
{
// Remainder of current element
int rem = arr[i] % k;

// If remainder with current element divides
// k into two halves.
if (2 * rem == k)
{
// Then there must be even occurrences of
// such remainder
if (freq[rem] % 2 != 0)
return false;
}

// If remainder is 0, then there must be two
// elements with 0 remainder
else if (rem == 0)
{
if (1 & freq[rem])
{
return false;
}
else
{
}
}

// Else number of occurrences of remainder
// must be equal to number of occurrences of
// k - remainder
else if (freq[rem] != freq[k - rem])
return false;
}
return true;
}

  
public static void main(String[] args) {

int a1[] ={1};

int a2[] = { 1,2 };
  
int a3[] = { 0,0,1 };
  
int a4[] = { 2,3,4 };
  
int a5[] = { 1,3,5,10 };
  
int a6[] = { 1,3,5,11 };
  
int a7[] = { 9,8,7,6,5,4,3,2,1 };
  
int a8[] = { 9,8,7,6,12,4,3,2,1 };
  
int i1[] = { 7 };
  
int i2[] = { 3,4 };
  
int i3[] = { 3,4,5 };
  
int i4[] = { 9,10,11 };
  
int o1[] = { 3,4 };
  
int o2[] = { 2,3,4 };
  
int o3[] = { 3,4,5,6 };
  
int o4[] = { 1,2,3,4,5,6 };
  
int s1[] = { 2, 2 };
  
int s2[] = { 2, 3 };
  
int s3[] = { 5, 2, 3 };
  
int s4[] = { 5, 2, 2 };
  
int s5[] = { 1, 1, 1, 1, 1, 1 };
  
int s6[] = { 1, 1, 1, 1, 1 };
  
int s8[] = { 1 };
  
int s9[] = { 3, 5 };
  
int s10[] = { 5, 3, 2 };
  
int s11[] = { 2, 2, 10, 10, 1, 1 };
  
int s12[] = { 1, 2, 2, 10, 10, 1, 1 };
  
int s13[] = { 1, 2, 3, 10, 10, 1, 1 };
  
  
System.out.println("Jones Robert ");
System.out.println("Assignment 3");
System.out.println("Recursion.");
System.out.println("All calls must result in true or false.");
System.out.println();

System.out.println("Double Or Nothing." );

System.out.println("1. " + doubleOrNothing(a1, 1,0) );
  
System.out.println( "2. " + doubleOrNothing(a2, 2,0) );
  
System.out.println("3. " + doubleOrNothing(a3, 3,0) );
  
System.out.println("4. " + doubleOrNothing(a4, 3,0));
  
System.out.println("5. " + doubleOrNothing(a5, 4,0) );
  
System.out.println("6. " + doubleOrNothing(a6, 4,0) );
  
System.out.println("7. " + doubleOrNothing(a7, 9,0) );
  
System.out.println("8. " + doubleOrNothing(a8, 9,0) );
  
System.out.println();
System.out.println();
  
System.out.println("Word Separator.");

System.out.println("1. " + wordSeparator("Y", "X", 4));

System.out.println("2. " + wordSeparator("Y", "X", 2));

System.out.println("3. " + wordSeparator("Y", "X", 1));

System.out.println("4. " + wordSeparator("Y", "X", 0));

System.out.println();
  
System.out.println("McNugget Numbers" );

System.out.println(" 1. " + mcNuggetNumber(0));

System.out.println(" 2. " + mcNuggetNumber(1) );

System.out.println(" 3. " + mcNuggetNumber(2) );

System.out.println(" 4. " + mcNuggetNumber(3) );

System.out.println(" 5. " + mcNuggetNumber(4) );

System.out.println(" 6. " + mcNuggetNumber(5) );

System.out.println(" 7. " + mcNuggetNumber(6) );

System.out.println(" 8. " + mcNuggetNumber(7) );

System.out.println(" 9. " + mcNuggetNumber(8) );

System.out.println("10. " + mcNuggetNumber(9) );

System.out.println("11. " + mcNuggetNumber(10) );

System.out.println("12. " + mcNuggetNumber(11) );

System.out.println("13. " + mcNuggetNumber(12) );

System.out.println("14. " + mcNuggetNumber(13));

System.out.println("15. " + mcNuggetNumber(14));

System.out.println("16. " + mcNuggetNumber(15));

System.out.println("17. " + mcNuggetNumber(16));

System.out.println();

System.out.println ("Split the Array");
System.out.println ("1. " + splitArray (1));
System.out.println ("2. " + splitArray (2));
System.out.println ("3. " + splitArray (3));
System.out.println ("4. " + splitArray (4));
System.out.println ("5. " + splitArray (5));
System.out.println ("6. " + splitArray (6));
System.out.println ("7. " + splitArray (7));
System.out.println ("8. " + splitArray (8));
System.out.println ("9. " + splitArray (9));
System.out.println ("10. " + splitArray (10));
System.out.println ("11. " + splitArray (11));
System.out.println ("12. " + splitArray (12));
System.out.println ("13. " + splitArray (13));
System.out.println ("14. " + splitArray (14));
System.out.println ("15. " + splitArray (15));
System.out.println ("16. " + splitArray (16));
System.out.println();

}

private static String splitArray(int i) {
throw new UnsupportedOperationException("Not supported yet."); //To change body of generated methods, choose Tools | Templates.
}
}

I have an error