Suppose that there are two independent economic factors, F1 and F2. The risk-free rate is 7%, and all stocks have independent firm-specific components with a standard deviation of 47%. Portfolios A and B are both well-diversified with the following properties: Portfolio Beta on F1 Beta on F2 Expected Return A 2.2 2.5 25 % B 2.8 –0.25 20 % What is the expected return-beta relationship in this economy?

Calculate the risk-free rate, rf, and the factor risk premiums, RP1 and RP2, to complete the equation below. (Do not round intermediate calculations. Round your answers to two decimal places.) E(rP) = rf + (βP1 × RP1) + (βP2 × RP2)

Consider the 7 steps of the Systems Development Life Cycle. What two steps in the process do you feel is the most critical? Can any steps be left out of the cycle?

• Planning

• Needs Analysis

• Design and Acquisition

• Build

• Testing

• Implementation

• Maintenance

uppose that there are two independent economic factors, F1 and F2. The risk-free rate is 7%, and all stocks have independent firm-specific components with a standard deviation of 37%. Portfolios A and B are both well-diversified with the following properties: Portfolio Beta on F1 Beta on F2 Expected Return A 1.3 1.7 27 % B 2.2 –0.17 24 % What is the expected return-beta relationship in this economy? Calculate the risk-free rate, rf, and the factor risk premiums, RP1 and RP2, to complete the equation below. (Do not round intermediate calculations. Round your answers to two decimal places.) E(rP) = rf + (βP1 × RP1) + (βP2 × RP2)

Suppose two independent random samples of sizes n1 = 9 and n2 = 7 that have been taken from two normally distributed populations having variances σ12 and σ22 give sample variances of s12 = 117 and s22 = 19. (a) Test H0: σ12 = σ22 versus Ha: σ12 ≠ σ22 with σ = .05. What do you conclude? (Round your answers to 2 decimal places.) F = F.025 = H0:σ12 = σ22 (b) Test H0: σ12 < σ22versus Ha: σ12 > σ22 with σ = .05. What do you conclude? (Round your answers to 2 decimal places.) F = F.05 = H0: σ12 < σ22

Suppose two independent random samples of sizes n1 = 9 and n2 = 7 that have been taken from two normally distributed populations having variances σ12 and σ22 give sample variances of s12 = 94 and s22 = 13. (a) Test H0: σ12 = σ22 versus Ha: σ12 ≠ σ22 with σ = .05. What do you conclude? (Round your answers to 2 decimal places.) F = F.025 = H0:σ12 = σ22 (b) Test H0: σ12 < σ22versus Ha: σ12 > σ22 with σ = .05. What do you conclude? (Round your answers to 2 decimal places.) F = F.05 = H0: σ12 < σ22

7. Two fair six sided dice are rolled.

(i) What is the probability that the sum of the two results is 6?
(ii) What is the probability that the larger value of the two results is 4?

(iii) What is the probability that the both results are at most 4?
(iv) What is the probability that the number 3 appears at least once?

WRITE A JAVA PROGRAM:

For this lab, you will create a 3 x 7 two dimensional array to store how many pounds of food three monkeys eats each day in a week. The 2D array is then passed to functions to find total, average and least amount of food consumption, etc. The program then need to display:

• the average amount of food the three monkeys ate per day

• the least amount of food eaten all week by any one monkey.

• each monkey's consumption of food during the week

• the average of food the 3 monkeys ate on Monday and Saturday.

The general structure of Lab9.java should be similar as follows:

import java.util.Scanner;
import java.text.DecimalFormat;

public class Lab9
{
    public static void main(String[] args)
    {
        //declare necessary constants and variables here
        //......

        //Create a 2D array to hold the pounds of food consumed
        //by each monkey on each day of the week
        //......

        //Use nested for loop to get data and fill in the 2D array
        //......

        //call the findGroupTotal() method and compute
        //the average amount of food the 3 monkeys ate per day
        //......

//call the findLeastAmtFood() method and compute
//the least amount of food eaten all week by any one monkey
//......

         //Find Monkey #1 total consumption of food during the week
        //......

        //Find Monkey #2 total consumption of food during the week
        //......

        //Find Monkey #3 total consumption of food during the week
        //......

        //Find the average of food the 3 monkeys eat on Monday
        //......

        //Find the average of food the 3 monkeys eat on Saturday
        //......
    } //end main()

    //This method takes a 2D array as input parameter and returns
    //the sum of all elements inside
    public static double findGroupTotal(double[][] a2DArray)
    {
        //......
    }

//This method takes a 2D array as input parameter and returns
//the smallest element inside
public static double findLeastAmtFood(double[][] a2DArray)
{
    //......
}

} //end of class

1.2 Step 2: Declare necessary variables, constants and a 2D array inside the main()

For this section of the lab, you will need to declare two (2) constants, both are integers, one for the number of monkeys (3), another for the number of days (7). You also need to declare a Scanner object that is used to read data from the user, and also a DecimalFormat object which will be used to format all double variables' output. Note: in this lab, all output need to be formatted with 2 decimal digits.

// For example, declare a constant that hold the number of monkeys.
final int NUM_MONKEYS = 3;

// declare a constant that hold the number of days (7 days).
// ----

// declare a Scanner object which will be used to get user input
// ----

// declare a DecimalFormat object which will be used to format the output
// ----

// declare and create a 2D array called 'food' that holds the pounds of food consumed
// by each monkey on each day of the week

// ----

As we learned in class, for example, to declare and create a two dimensional array, the syntax is as follows.

data_type[][] ArrayName = new data_type[NUM_OF_ROWS][NUM_OF_COLUMNS];

For Lab9, the data type is the pounds of food each monkey ate on a specific day; ArrayName as mentioned above, is food, the number of rows corresponds to number of the monkeys, and the number of columns corresponds to number of days in a week.

1.3 Step 3: Read in data from user and fill in the 2D array

Next, use the Scanner object created in the previous step to ask the user to enter the pounds of food ate by each of the 3 monkeys in each day of the week. i.e. we will need to fill in the 2D array 'food' we created in the previous step row-by-row, and for each row, we need to fill in the data from left to right. Remeber that we should always print a message indicating what is to be input before requesting information from the user. To do this task, we will need to write a nested for loop, the outer for loop iterates on each of the monkeys, where the inner for loop iterates on each of the day in one week.

for (/* loop logic - iterate on each of the 3 monkeys */)
{
    System.out.print("\nEnter pounds of food eaten by monkey #" + //---- + " on \n");
    for (/*loop logic - iterate on each day of the week */)
        {
        System.out.print( " on day " + //---- + ": ");
        //use Scanner object to get user input and store it inside 2D array 'food'
        food[monkey][day] = scan.nextDouble();
        }
}

//Codes in step #6 to step #8 continue......

1.4 Step 4: Design the findGroupTotal() method

Up to above step 3, codes should be put inside the main() method. In order to call findGroupTotal() method in main(), we need to design findGroupTotal() first. This method need to be put outside of the main(), but within the same class. The header of the method is as follows:

public static double findGroupTotal(double[][] a2DArray)

Basically this method takes a two dimensional array as input and returns the sum of all its elements inside. As we learned in class, in order to do this, we will need to write a nested for loop, the outer for loop iterates on each of the rows, where the inner for loop iterates on each of the columns of the 2D array. Very similar as we did in step #3. Note:

• a2DArray.length equals to the number of rows
• a2DArray[0].length equals to the number of columns.

double total = 0.0;

for (/* loop logic - iterate on each of the row */)
{
    for (/* loop logic - iterate on each of the colunms */)    
        total += a2DArray[row][column];
}
return total;

1.5 Step 5: Design the findLeastAmtFood() method

Similar as we did in step #4, in order to call findLeastAmtFood() method in main(), we need to design findLeastAmtFood() method first. This method need to be put outside of the main(), but inside the Lab9.java class. The header of the method is as follows:

public static double findLeastAmtFood(double[][] a2DArray)

Basically this method takes a two dimensional array as input and returns the smallest elements inside. As we learned in class, in order to do this, we will need to write a nested for loop, the outer for loop iterates on each of the rows, where the inner for loop iterates on each of the columns of the 2D array. Very similar as we did in step #4, except that we need to declare and intialize a local variable leastAmt as follows:

double leastAmt = a2DArray[0][0];

for (/* loop logic - iterates on each of the rows */)
{
    for (/* loop logic - iterate on each of the columns */)
        {
        if (a2DArray[row][column] < leastAmt)
            //replace leastAmt with the two-D array element at (row, column)
        }

}
return leastAmt;

1.6 Step 6: Call findGroupTotal()and findLeastAmtFood() methods in main()

Continue on what we have left in step 4, now we need to call findGroupTotal() and  findLeastAmtFood() methods on the two-dimensional array food. Since both method returns a double value, you might need to declare any necessary variables to hold the returned value, such as the following:

double groupTotal;

When we call a method with 2D array as input parameter, we just need to plug in the actual parameter's name, such as the following:

groupTotal = findGroupTotal(food);    //find total on 2D array food

Next, you need to do simple computation to find the average amount of food ate per day by the entire family of monkeys, which equals to the groupTotal divided by number of days, then output the computation result according to the test cases.

Similarly, call findLeastAmtFood()method on two dimensional array food, declare any necessary local variables here and output the result as test cases show.

1.7 Step 7: Find each of the monkey's consumption of food during the week

Still inside the main() method, for 2D array food, we need to find the sum of each of the rows, this corresponds to each of the monkeys' consumption of food in the whole week. Use monkey #1 as an example, first we declare a local variable totalOne which will be used to hold monkey #1's total consumption,

double totalOne = 0.0;

Next, we write a for loop which iterates on each of the days in a week (column of 2D array food) and sum the elements one-by-one as follows:

for (int day = 0; day < NUM_DAYS; day++)
    totalOne += food[0][day];

we then output the result on screen:

System.out.print("\nMonkey #1 eat total of " + fmt.format(totalOne) + " pounds of food in this week.\n");

//Follow above monkey #1's example, compute and output monkey #2 & #3's total consumption of food in one week

//----

1.8 Step 8: Find the average of food the 3 monkeys eat on Monday and Saturday

Continue on above step 7, we now need to find the total amount of food the 3 monkeys ate on Monday or Saturday, this corresponds to sum of all elements in column 0 and 5 of 2D array food respectively. Always keep in mind that index starts from 0!

Let's compute the average of food the three monkeys ate on Monday first, we declare a local variable totalMonday which will be used to hold the total consumption, on Monday

double totalMonday = 0.0;

Next, we need to write a for loop which iterates on each of the monkeys on Monday (row of 2D array food), note for Monday, the column index is 0,

for (int monkey = 0; monkey < 3; monkey ++)
        totalMonday += food[monkey][0];

Last, we compute the average and output accordingly,

double averageMon = totalMonday / 3.0;

//Follow above Monday example, compute and output the average of food the three monkeys consumed on Saturday.

//----

Suppose two independent random samples of sizes n1 = 9 and n2 = 7 that have been taken from two normally distributed populations having variances σ12 and σ22 give sample variances of s12 = 94 and s22 = 13. (a) Test H0: σ12 = σ22 versus Ha: σ12 ≠ σ22 with σ = .05. What do you conclude? (Round your answers to 2 decimal places.) F = 7.231 F.025 = H0:σ12 = σ22 (b) Test H0: σ12 < σ22versus Ha: σ12 > σ22 with σ = .05. What do you conclude? (Round your answers to 2 decimal places.) F = 4.147 F.05 = H0: σ12 < σ22

You are the manager of a 40 head broodmare farm. The mare’s average weight is 1,000 lbs. ➢ You know the mares in early lactation require: 28.3 Mcal DE, 3 lbs Crude protein, 50 g Ca, 34 g P. ➢ You go to the local feed store and purchase a feed that sells of $8.50/50 lb bag. ➢ The nutrient make up of the feed is: 13.5% CP, 0.5% Ca, and 0.44% P. By the fiber content you estimate the DE to be around 1.3 Mcal/lb. ➢ You feed 1% bwt in grass hay (7% CP, 0.8 Mcal DE/lb, 0.4% Ca, 0.2% P) A. How much of the commercial feed must you feed to meet the mares’ requirements (per head, per day)? 21.76 B. If the hay costs $40/ton, what is the monthly cost to feed these 40 mares, in early lactation (grain cost is given above)? a. Hay b. Grain c. Total

            You have decided to open a restaurant in Huntington. The following table gives the payoffs based on two states of nature, favorable and unfavorable demand. You     believe that the probability of a favorable market is 0.8. You can open any one of        three different sizes of restaurant.     

            You have decided to do some marketing research (using the skills that you learned). If the marketing research is positive (probability = .7), then the probability of favorable demand goes to .95. If the marketing research is negative (shows weak demand) (probability of .3), then the probability of favorable demand goes to .40.

1. Using all of the information, what should you do? Provide calculations.

2. What is the expected value of perfect information?

3. What is the expected value of sample information?