Three resistors with resistances R₁, R₂, R₃ are connected in parallel across a battery with voltage V. By Ohm’s law, the current (amps) is

I = V* [ (1/R₁) + (1/R₂) + (1/R₃) ]

Assume that R₁, R₂, R_3, and V are independent random variables

where R₁ ~ Normal (m = 10 ohms, s = 1.5 ohm)

            R₂ ~ Normal (m = 15 ohms, s = 1.5 ohm)

            R₃ ~ Normal (m =20 ohms, s = 1.0 ohms)

            V ~ Normal (m = 120 volts, s = 2.0 volts

(a) Use Monte Carlo Simulation (10,000 random draws from each input random variable) to estimate the mean and standard deviation of the output variable current. (b) Assess whether the output variable current is normally distributed. (c) Assess whether the inverse of current squared (1/ I2 ) is normally distributed. (d) Estimate the probability that the current is less than 25 amps assuming that the inverse of current squared is normally distributed. (e) Compare your answer to (d) with your simulation results – how many of the 10,000 random results for current are below 25 amps via the Stat > Tables > Tally command?

Ginny is endowed with $ 8million and is deciding whether to invest in a restaurant. Assume perfect capital markets with an interest rate of 6%.

1. List 4 perfect capital market assumptions.

1.   ______________________________      2.   ______________________________

3.   ______________________________ 4.   _______________________________

2. Which investment option should Ginny choose?

3. Which investment option can be eliminated from consideration? Why?

Ginny is actively pursuing another business venture as a ticket scalper. She estimates that for a $2 million investment in inventory she can resell her tickets for $6 million over the next two years (cash flows realized in exactly two years). Assume the same 6% interest rate.

4. What is the NPV of the Ticket Brokering venture?

5. What is the new value of Ginny’s Corporation?

6. Suppose Ginny does not have the $2 million to start the new venture. Instead, she wants to raise equity capital by issuing 100,000 shares. What price will new investors be willing to pay?

Question 5 (25 marks / Risk, Return and CAPM)
(Each of the following parts is independent.)
(a) According to the Capital Asset Pricing theory, what return would be required by an investor whose portfolio is made up of 40% of the market portfolio (m) and 60% of Treasury bills (i.e. risk-free asset)? Assume the risk-free rate is 3% and the market risk premium is 7%?  

(b) You are considering investing in the following two stocks. The risk-free rate is 7 percent and the market risk premium is 8 percent.

Stock ,Price Today , Expected Price in 1 year, Expected Dividend in 1 year, Beta
X $20 $22 $2.00 1.0
Y $30 $32 $1.78 0.9

i) Compute the expected and required return (using CAPM) on each stock.   
ii) Which asset is worth investing? Support your answer with calculations.     

(c) Which pair of stocks used to form a 2-asset portfolio would have the greatest diversification effect for the portfolio? Briefly explain.
                   
                            Correlation
Stocks A & B            -0.66
Stocks A & C            -0.42
Stocks A & D                0
Stocks A & E               0.75
         
(d) Explain the terms systematic risk and unsystematic risk and their importance in determining investment return.          

(Each of the following parts is independent.)

1. According to the Capital Asset Pricing theory, what return would be required by an investor whose portfolio is made up of 40% of the market portfolio (m) and 60% of Treasury bills (i.e. risk-free asset)?  Assume the risk-free rate is 3% and the market risk premium is 7%?

2. You are considering investing in the following two stocks. The risk-free rate is 7 percent and the market risk premium is 8 percent.

1. Compute the expected and required return (using CAPM) on each stock.
2. Which asset is worth investing? Support your answer with calculations.

3. Which pair of stocks used to form a 2-asset portfolio would have the greatest diversification effect for the portfolio? Briefly explain.

(d)   Explain the terms systematic risk and unsystematic risk and their importance in determining investment return.

Please provide stepping for all if possible, much appreciated.

Question 5 (25 marks / Risk, Return and CAPM) (Each of the following parts is independent.) (a) According to the Capital Asset Pricing theory, what return would be required by an investor whose portfolio is made up of 40% of the market portfolio (m) and 60% of Treasury bills (i.e. risk-free asset)? Assume the risk-free rate is 3% and the market risk premium is 7%? ​​​​ (b) You are considering investing in the following two stocks. The risk-free rate is 7 percent and the market risk premium is 8 percent. Stock Price Today Expected Price in 1 year Expected Dividend in 1 year Beta X $20 $22 $2.00 1.0 Y $30 $32 $1.78 0.9 i) Compute the expected and required return (using CAPM) on each stock. ii) Which asset is worth investing? Support your answer with calculations. (c) Which pair of stocks used to form a 2-asset portfolio would have the greatest diversification effect for the portfolio? Briefly explain. Correlation Stocks A & B -0.66 Stocks A & C -0.42 Stocks A & D 0 Stocks A & E 0.75 ​​​​​​​​​​​ (d)​Explain the terms systematic risk and unsystematic risk and their importance in determining ​investment return.​​​​​​

1.) First Question on Class – the class Circle Given the code below, modify it so that it runs. This will require you to add a class declaration and definition for Circle. For the constructor of Circle that takes no arguments, set the radius of the circle to be 10. You are to design the class Circle around the main method. You may NOT modify the body of the main method in anyway, if you do your code WILL NOT BE ACCEPTED, AND WILL BE GRADED AS ALL WRONG. For this question, YOU MUST capture the output of a run of your program and submit it with your source code as your solution. (TIP: the formula to find the area of a Circle is pi times r squared, or PI * r * r).

#include using namespace std;

const float PI = 3.1416; i

nt main() {

Circle c1, c2, c3; c

1.setRadius(1.0);

c3.setRadius(4.5);

Circle circles[] = {c1, c2, c3};

for (int i = 0; i < 3; i++) {

float rad, diam, area;

Circle c = circles[i];

rad = c.getRadius();

diam = c.getDiameter();

area = c.getArea();

cout << "circle " << (i) << " has a radius of: " << rad << ", a diameter of: " << diam << ", and an area of: " << area << endl;

}

return 0;

The language is C++, thanks in advance

Copy the program Stats.java to your computer and implement the TBI (To Be Implemented) stats() and checkIfSorted() methods following the instructions given in their method comment blocks.

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Stats.java

import java.util.*;

/*
 * This Java application calculates some statistics
 * given an array of integers.
 *
 * @creator gdt
 * @created 02017.12.15
 * @updated 02019.01.21  morphed the assignment
 */

interface StatsConstants {
   // used by print() to format output...
   String PRINT_BEGIN = "[";
   String PRINT_END = "]";
   String PRINT_SEPARATOR = ",";

   // checkIfSorted() return values...
   int UNSORTED = 0;
   int ASCENDING = 1;
   int DESCENDING = 2;
   int SKIP = 3;
}

public class Stats {

   public static void main(String[] argv) {

      int[][] data = { 
         null,
         { },
         { 0 },
         { 1, 2 },
         { 1, 1 },
         { 1, 3, 2 },
         { 5, 5, 5, 5, 5 },
         { 2, 0, 5, 4, 8, 5 },
         { 1, 5, 6, 6, 6, 7, 9 },
         { -7, 0, 0, 3, 3, 3, 4, 4 },
         { -2, -2, 0, 1, 1, 2, 2, 2 },
         { -4, -2, 42, 12, 12, 3, -2 },
      };
      for (int i = 0; i < data.length; i++) {
         switch (checkIfSorted(data[i])) {
            case StatsConstants.SKIP:
               if (data[i] == null)
                  System.out.println("null element\n");
               else if (data[i].length == 0) 
                  System.out.println("empty array\n");
               else
                  System.out.println("???\n");
               continue;
            case StatsConstants.UNSORTED:
               Arrays.sort(data[i]);
               break;
            case StatsConstants.DESCENDING:
               reverseArray(data[i]);
               break;
         }
         printResults(stats(data[i]));
      }
   }

   private static void reverseArray(int[] x) {
      for (int i = 0, j = x.length - 1 ; i < j; i++, j--) {
         int k = x[i];
         x[i] = x[j];
         x[j] = k;
      }
   }

   private static void printArray(int[] x, boolean nl) {
      System.out.print(StatsConstants.PRINT_BEGIN);
      for (int i = 0, j = x.length - 1; i < j; i++)
         System.out.print(x[i] + StatsConstants.PRINT_SEPARATOR);
      System.out.print(x[x.length - 1] + StatsConstants.PRINT_END);
      if (nl) System.out.println();
   }

   private static void printResults(Results r) {
      printArray(r.data, true);
      StringBuffer sb = new StringBuffer("...mean: ");
      sb.append(r.mean).append("; median: "). append(r.median).
         append("; mode: "). append(r.nomode ? "modeless" : r.mode).
         append("; cardinality: ").append(r.cardinality).
         append("; range: ").append(r.range);
      System.out.println(sb);
      System.out.println();
   }

   static class Results {
      public int[] data; 
      public int cardinality;
      public int range;
      public double mean;
      public double median;
      public int mode;
      public boolean nomode;
   }

   /*
    * TBI (To Be Implemented)...
    *
    * Instantiates and returns a Results object that
    * contains the calculations (statistics) for the 
    * int[] parameter.  
    *
    * Note: 'mode' is a single solitary number repeated 
    * more often than any other number. The Results object
    * nomode variable is set to true if there is no mode.
    *
    * The stats() method assumes the int[] is sorted
    * in ascending order.
    *
    * @param data  an array if ints
    * @return a Results object
    */
   private static Results stats(int[] data) {
      
   }

   /*
    * TBI (To Be Implemented)...
    *
    * Checks if the contents of the int[] parameter is sorted.
    * The method returns values defined in interface StatsConstants.
    *
    * @param  data  an array of integers
    * @return SKIP if data is null or the array is empty;
    *         else UNSORTED or DESCENDING or ASCENDING
    */
   private static int checkIfSorted(int[] data) {

   }

}

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

The program output must match the following. Note: Every output line that starts with ... is followed by a blank line:

null element

empty array

[0]
...mean: 0.0; median: 0.0; mode: 0; cardinality: 1; range: 0

[1,2]
...mean: 1.5; median: 1.5; mode: modeless; cardinality: 2; range: 1

[1,1]
...mean: 1.0; median: 1.0; mode: 1; cardinality: 2; range: 0

[1,2,3]
...mean: 2.0; median: 2.0; mode: modeless; cardinality: 3; range: 2

[5,5,5,5,5]
...mean: 5.0; median: 5.0; mode: 5; cardinality: 5; range: 0

[0,2,4,5,5,8]
...mean: 4.0; median: 4.5; mode: 5; cardinality: 6; range: 8

[1,5,6,6,6,7,9]
...mean: 5.714285714285714; median: 6.0; mode: 6; cardinality: 7; range: 8

[-7,0,0,3,3,3,4,4]
...mean: 1.25; median: 3.0; mode: 3; cardinality: 8; range: 11

[-2,-2,0,1,1,2,2,2]
...mean: 0.5; median: 1.0; mode: 2; cardinality: 8; range: 4

[-4,-2,-2,3,12,12,42]
...mean: 8.714285714285714; median: 3.0; mode: modeless; cardinality: 7; range: 46

The data shown to the right represent the age​ (in weeks) at which babies first​ crawl, based on a survey of 12 mothers. Complete parts​ (a) through​ (c) below. 52 30 44 35 47 37 56 26 54 44 35 28 Click here to view the table of critical t-values. LOADING... Click here to view page 1 of the standard normal distribution table. LOADING... Click here to view page 2 of the standard normal distribution table. LOADING... ​(a) Draw a normal probability plot to determine if it is reasonable to conclude the data come from a population that is normally distributed. Choose the correct answer below. A. 20 30 40 50 60 -2 -1 0 1 2 Age (in weeks) Expected z-score A normal probability plot has a horizontal axis labeled "Age (in weeks)" from 20 to 60 in increments of 5 and a vertical axis labeled "Expected z-score" from negative 2 to 2 in increments of 0.5. The graph contains 12 plotted points that follow the general pattern of a line that falls from left to right through (30, 1) and (50, negative 1), with slight deviation from the line pattern at the tails. The 12 plotted points have coordinates as follows: (26, 1.6); (28, 1.1); (30, 0.8); (35, 0.5); (35, 0.3); (37, 0.1); (44, negative 0.1); (44, negative 0.3); (47, negative 0.5); (52, negative 0.8); (54, negative 1.1); (56, negative 1.6). All coordinates are approximate. B. 20 30 40 50 60 -4 -2 0 2 4 Age (in weeks) Expected z-score A normal probability plot has a horizontal axis labeled "Age (in weeks)" from 20 to 60 in increments of 5 and a vertical axis labeled "Expected z-score" from negative 4 to 4 in incrementservals of 1. The graph contains 12 plotted points that follow the general pattern of a line that rises from left to right through (30, negative 2) and (50, 2), with slight deviation from the line pattern at the tails. The 12 plotted points have coordinates as follows: (26, negative 3.3); (28, negative 2.3); (30, negative 1.6); (35, negative 1); (35, negative 0.6); (37, negative 0.2); (44, 0.2); (44, 0.6); (47, 1); (52, 1.6); (54, 2.3); (56, 3.3). All coordinates are approximate. C. 20 30 40 50 60 -2 -1 0 1 2 Age (in weeks) Expected z-score A normal probability plot has a horizontal axis labeled "Age (in weeks)" from 20 to 60 in increments of 5 and a vertical axis labeled "Expected z-score" from negative 2 to 2 in incrementstervals of 0.5. The graph contains 12 plotted points that follow the general pattern of a line that rises from left to right through (30, negative 1) and (50, 1), with slight deviation from the line pattern at the tails. The 12 plotted points have coordinates as follows: (26, negative 1.6); (28, negative 1.1); (30, negative 0.8); (35, negative 0.5); (35, negative 0.3); (37, negative 0.1); (44, 0.1); (44, 0.3); (47, 0.5); (52, 0.8); (54, 1.1); (56, 1.6). All coordinates are approximate. D. 20 30 40 50 60 -4 -2 0 2 4 Age (in weeks) Expected z-score A normal probability plot has a horizontal axis labeled "Age (in weeks)" from 20 to 60 in increments of 5 and a vertical axis labeled "Expected z-score" from negative 4 to 4 in increments of 1. The graph contains 12 plotted points that follow the general pattern of a line that falls from left to right through (30, 2) and (50, negative 2), with slight deviation from the line pattern at the tails. The 12 plotted points have coordinates as follows: (26, 3.3); (28, 2.3); (30, 1.6); (35, 1); (35, 0.6); (37, 0.2); (44, negative 0.2); (44, negative 0.6); (47, negative 1); (52, negative 1.6); (54, negative 2.3); (56, negative 3.3). All coordinates are approximate. Is it reasonable to conclude that the data come from a population that is normally​ distributed? A. ​Yes, because the plotted values are approximately linear. B. ​No, because the plotted values are not linear. C. ​No, because there are not enough values to make a determination. D. ​Yes, because the plotted values are not linear. ​(b) Draw a boxplot to check for outliers. Choose the correct answer below. A. 20 30 40 50 60 A boxplot has a horizontal axis labeled from 20 to 60 in increments of 5. The boxplot has the following five-number summary: 26, 32.5, 40.5, 49.5, 56. All values are approximate. B. 20 30 40 50 60 A boxplot has a horizontal axis labeled from 20 to 60 in increments of 5. The boxplot has the following five-number summary: 26, 32.5, 45, 54, 56. All values are approximate. C. 20 30 40 50 60 A boxplot has a horizontal axis labeled from 20 to 60 in increments of 5. The boxplot has the following five-number summary: 26, 37, 40.5, 49.5, 56. All values are approximate. D. 20 30 40 50 60 A boxplot has a horizontal axis labeled from 20 to 60 in increments of 5. The boxplot has the following five-number summary: 26, 37, 45, 54, 56. All values are approximate. Does the boxplot suggest that there are​ outliers? A. ​No, there are no points that are greater than the third quartile or less than the first quartile. B. ​Yes, there is at least one point that is greater than the third quartile or less than the first quartile. C. ​Yes, there is at least one point that is outside of the​ 1.5(IQR) boundary. D. ​No, there are no points that are outside of the​ 1.5(IQR) boundary. ​(c) Construct and interpret a 95​% confidence interval for the mean age at which a baby first crawls. Select the correct choice and fill in the answer boxes to complete your choice. ​(Round to one decimal place as​ needed.) A. The lower bound is nothing weeks and the upper bound is nothing weeks. We are 95​% confident that the mean age at which a baby first crawls is outside of the confidence interval. B. The lower bound is nothing weeks and the upper bound is nothing weeks. We are 95​% confident that the mean age at which a baby first crawls is within the confidence interval. Click to select and enter your answer(s).

October

1. S. Erickson invested $5 0,000 cash, a $16,000 pool equipment, and $12,000 of office equipment in the company.

2. The company paid $4,000 cash for five months’ rent.

3. The company purchased $1,620 of office supplies on credit from Todd’s Office Products.

5. The company paid $4,220 cash for one year’s premium on a property and liability insurance policy.

6. The company billed Deep End Co $4,800 for services performed in installing a new pool

8. The company paid $1,620 cash for the office supplies purchased from Todd’s Office Products on October 3.

10. The company hired Julie Kruit as a part-time assistant for $136 per day, as needed.

12. The company billed Deep End Co another $1,600 for services performed.

15. The company received $4,800 cash from Deep End Co as partial payment on its account.

17. The company paid $750 cash to repair pool equipment that was damaged when moving it.

20. The company paid $1,958 cash for advertisements published in the local newspaper.

22.The company received $1,600 cash from Deep End Co. on its account.

28. The company billed Happy Summer Corp $6,802 for consulting services performed.

31. The company paid $952 cash for Julie Kruit’s wages for seven days’ work.

31. S. Ericksonwithdrew $3,500 cash from the company for personal use.

November

1. The Company reimbursed S. Erickson in cash for business automobile mileage allowance (Ericksonlogged 1,500 miles at $0.32 per mile).

2. The company received $5,630 cash from Underground Inc. for consulting services performed.

5. The company purchased office supplies for $1,325 cash from Todd’s Office Products.

8. The company billedSlides R Us $7,568 for services performed.

13. The company agreed to perform future services for Henry’s Pool and Spa Co. No work has been performed.

18. The company received $2,802 cash from Happy Summer Corp as partial payment of the October 28 bill.

22. The company donated $450 cash to the United Way in the company’s name.

24. The company completed work and sent a bill for $4,800toHenry’s Pool and SpaCo.

25. The company sent another bill to Happy Summer Corp for the past-due amount of $ 4 000.

28. The company reimbursed S. Erickson in cash for business automobile mileage(1,300 miles at $0.32 per mile).

30. The company paid cash to Julie Kruit for 14 days’ work.

30. S. Erickson withdrew $1,500 cash from the company for personal use

December

2. Paid $1,200 cash to West Side Mall for Splashing Around’s share of mall advertising costs.

3. Paid $350 cash for minor repairs to the company’s pool equipment

4. Received $4,800 cash from Henry’s Pool and Spa Co. for the receivable from November.

10. Paid cash to Julie Kruit for six days of work at the rate of $136 per day.

14. Notified by Henry’s Pool and Spa Co. that Splashing Around’s bid of $ 10,000 on a proposed project has been accepted. Henry’s paid a $ 6,500 cash advance to Splashing Around

15. Purchased $1,400 of office supplies on credit from Todd’s Office Products.

16. Sent a reminder to Slides R Us to pay the fee for services recorded on November 8.

20. Completed a project for Underground Inc and received $6,545 cash.

22–26 Took the week off for the holidays.

28. Received $4,500 cash from Slides R Us on its receivable.

29. Reimbursed S. Erickson for business automobile mileage (500 miles at $0.32 per mile).

31. S.Erickson withdrew $ 2,500 cash from the company for personal use.

Adjusting Entries

The following additional facts are collected for use in making adjusting entries prior to preparing

financial statements for the company’s first three months:

a. The December 31 inventory count of office supplies shows $1800 still available.

b.Three months have expired since the 12-month insurance premium was paid in advance.

c. As of December 31, Julie Kruit has not been paid for four days of work at $136 per day.

d.The pool equipment, acquired on October 1, is expected to have a four-year life with no salvage value.

e. The office equipment, acquired on October 1, is expected to have a five-year life with no salvage value.

f.Three of the five months’ prepaid rent has expired

just the adjusting entries journalized.