Which of the following set of quantum numbers (ordered n, ℓ, mℓ, ms) are possible for an electron in an atom?

Select all that are possible.

4, 3, -2, -1/2

4, 1, +2, +1/2

1, 0, 0, 0

3, 2, -2, -1/2

2, 1, 0, +1

Project#2 - ANOVA - Outline

Project#2 is based on Exercise 9.32 (Page 522). The case scenario and data are from it. Feel free to use SPSS, SAS and/or Excel (or any other standard statistical software) for data analysis. The data set is available on Blackboard (under Projects). There are three questions in that exercise. Beyond those questions, your paper must address the following:

I. Introduction

1. Explain the case and issues in it in your own words. [Use not more than 250 words.]

2. Explain the goals of the study in your own words. [Not more than 150 words.]

II. Theory and concepts

1. What type of study is this? Observational or experimental study? Why? Explain. [Not more than          

      150 words.]

2. Identify the variables and explain their nature (such as qualitative or quantitative) and their

      relationships. [Not more than 150 words.]

3. Explain the factor/factors and factor levels, and also independent and dependent variables used in

     the study. [Not more than 150 words.]

4.   What are the major assumptions in your ANOVA analysis? [As many words as necessary.]

5.   How will you test the assumptions? [As many words as necessary.]

III. Hypothesis and Critical Value

1. State the null ad alternate hypothesis. Briefly explain the hypothesis. [Not more than 150 words.]

2. Find F_Critical. What is the meaning of it? Briefly explain how you found it. [Not more than 150 words.]

IV. Data Analysis

Using the software conduct the following analysis and explain the major findings:

1. Generate descriptive statistics of the variables. Explain the major findings. How do they relate to the

      ANOVA analysis. [Not more than 250 Words.]

2. Generate histograms, box Plots and Q-Q Plot for the variables. Explain the major findings. How do

      they relate to the ANOVA analysis? [Not more than 250 words.]

3. Conduct the ANOVA analysis. Explain the findings. [As many words as necessary.]

4. What are your conclusions from the analysis? Explain. [As many words as necessary.]

IV. Decisions

As a researcher what decision will you draw from this study? Why? Explain. [Not more than 200 words.]

Report on the Project

Write a report, following the steps given above. The report must include a simple title page. Also, include the software printouts. Submit your report on Blackboard (Project_2 Dropbox).

DATA:

Find the general solution to the equation

?″+4?=1

summarize the chapters 1-4 of the scarlet letter

Question 20

1. Like many high school seniors, Anne has several universities to consider when making her final college choice. To assist in her decision, she has decided to use AHP to develop a ranking for school R, school P, and school M. The schools will be evaluated on five criteria, and Anne's pair-wise comparison matrix for the criteria is shown below.
   

The universities' pair-wise comparisons on the criteria are shown below

1. Distance	R	P	M
   R	1	2	3
   P	1/2	1	3/2
   M	1/3	2/3	1

   Programs	R	P	M
   R	1	1/2	1
   P	2	1	2
   M	1	1/2	1

   Size	R	P	M
   R	1	4	2
   P	1/4	1	1/2
   M	1/2	2	1

   Climate	R	P	M
   R	1	1	3
   P	1	1	3
   M	1/3	1/3	1

   Cost	R	P	M
   R	1	1/5	1
   P	5	1	5
   M	1	1/5	1

   
   What is the overall priority of the three universities?

   University Priority R 0.5714 P 0.1429 M 0.2857
   		University Priority R 0.2500 P 0.5000 M 0.2500
   		University Priority R 0.3705 P 0.4030 M 0.2265
   		University Priority R 0.5455 P 0.2727 M 0.1818
   		University Priority R 0.4286 P 0.4286 M 0.1428

Problem 3:

Find the equilibrium distribution for each transition matrix.

a)

1/2 1/9 3/10

1/3 1/2 1/5

1/6 7/18 1/2

b)

2/5 0   3/4

0 2/3 1/4

3/5 1/3 0

Problem 4:

For either transition matrix in problem 3, find the other two eigenvalues with corresponding eigenvectors.

Problem 3:

Find the equilibrium distribution for each transition matrix.

a)

1/2 1/9 3/10

1/3 1/2 1/5

1/6 7/18 1/2

b)

2/5 0   3/4

0 2/3 1/4

3/5 1/3 0

Problem 4:

For either transition matrix in problem 3, find the other two eigenvalues with corresponding eigenvectors.

/**
 * This program will sort an n by n array by the first value in each row.
 * Selection sort algorithm is modified to do the sorting.
 * For example:
 * <p/>
 * If the original array is:
 * 1  2  3  4  5
 * 3  4  5  1  2
 * 5  2  3  4  1
 * 2  3  1  4  5
 * 4  2  3  1  5
 * <p/>
 * The array after sorting is:
 * 1  2  3  4  5
 * 2  3  1  4  5
 * 3  4  5  1  2
 * 4  2  3  1  5
 * 5  2  3  4  1
 *
 * @author YOUR NAME
 * @version 09/29/2020
 */
public class ArraySortByFirst
{
    private int[][] dataToSort;

    public ArraySortByFirst(int[]... data)
    {
        this.dataToSort = data;
    }

    /**
     * Task: Sorts an array of integers by the first value of each row. After
     * sorting, the first column of the array is in ascending order.
     */
    public void sortByFirstColumn()
    {
        //TODO Project2
        // I am similar to selection sort");

    }

    /**
     * Task: Finds the row of the smallest value in the first column of this.dataToSort array.
     *
     * @param first the index of the first array row to consider
     * @param last  the index of the last array row to consider
     * @return the index of the row with the smallest element in the first column among
     * this.dataToSort[first], this.dataToSort[first + 1], . . . , this.dataToSort[last]
     */
    private int getIndexOfSmallest(int first, int last)
    {
        int min = this.dataToSort[first][0];
        int indexOfMin = first;

        //TODO Project2

        return indexOfMin;
    }

    /**
     * Task: Swaps the rows  this.dataToSort[i] and this.dataToSort[j].
     *
     * @param i row to swap
     * @param j row to swap
     */
    private void swap(int i, int j)
    {

        //TODO Project2

    }

    /**
     * Task: displays the content of this.dataToSort row by row
     */
    public void display()
    {

        //TODO Project2 - implement first;


    }

    public static void main(String args[])
    {
        int array[][] = {{1, 2, 3, 4, 5}, {3, 4, 5, 1, 2}, {5, 2, 3, 4, 1}, {2, 3, 1, 4, 5}, {4, 2, 3, 1, 5}};

        ArraySortByFirst sortArray = new ArraySortByFirst(array);
        System.out.println("The original array is ");
        sortArray.display();
        System.out.println();

        sortArray.sortByFirstColumn();
        System.out.println("The array after sorting is ");
        sortArray.display();
        System.out.println();
    } // end main
} // end ArraySortByFirst

Given an array ? of numbers and a window size ?, the sliding window ending at index ? is the subarray ?[? − ? + 1], ⋯ , ?[?] if ? ≥ ? − 1, and ?[0], ⋯ , ?[?] otherwise. For example, if ? = [0, 2, 4, 6, 8] and ? = 3, then the sliding windows ending at indices 0, 1, 2, 3 and 4 are respectively [0], [0, 2], [0, 2, 4], [2, 4, 6], and [4, 6, 8]. Write a method, movingAverage, that given as input an array ? of numbers and a window size ?, returns an array ? with the same length as ?, such that for every index ?, ?[?] is the average of the numbers in the sliding window ending at index ?. The skeleton for the method is provided in the file MovingAverage.java.

The following is a sample run.

Input:      ? = [0,2, 4, 6, 8],   ? = 3

Return:   [0, 1, 2, 4, 6]

Explanation: As explained above, the sliding windows at indices 0, 1, 2, 3 and 4 are respectively

[0], [0,2], [0, 2, 4], [2, 4, 6], and [4, 6, 8]. The average of the numbers in these sliding windows are respectively = 0, = 1, = 2, = 4, and = 6.

Your method must have time complexity ?(?), where ? is the length of the input array ?.

Hint: You may find a queue useful.

public class MovingAverage {

   public double[] movingAverage(int[] A, int w) {
      
       //Replace this line with your return statement
       return null;
   }

}

4. Sampling Without Replacement

We have n−2 beer bottles b1,…,bn−2 and 2 cider bottles c1 and c2 . Consider a uniformly random permutation π1,…,πn of these n bottles (so that each of the n! permutations is equally likely).

1. Let X be the index of the first beer bottle in the permutation. That is, {π1,…,πX−1}⊆{c1,c2} and πX∈{b1,…,bn} . What is E[X] ?
2. Let Y be the index of the first cider bottle in the permutation. That is {π1,…,πY−1}⊆{b1,…,bn} and πX∈{c1,c2} . What is E[Y] ?