Calculate the value of the stream of cash flows below in Year 4. t=0--->CF0 = $450 t=1--->CF1 = $550 t=2--->CF2 = $650 t=3--->CF3 = $750 t=4--->CF4 = $850 t=5--->CF5 = $950 t=6--->CF6 = $1050 The relevant rate is 8%.

The table below is a discrete probability distribution of study hours for mathematics in a given week.

1. Find the probability of x=3.
2. Find the mean and the standard deviation of this probability distribution.
3. Find the probability that x is at most 4 hours.

Gomi Waste Disposal is evaluating a project that would last for 4 years. The project’s internal rate of return is 8.18 percent; its NPV is 8,920 dollars; and the expected cash flows are -56,800 dollars at time 0, 10,500 dollars in 1 year, 46,300 dollars in 2 years, and X in 4 years. What is X?

Assignment 5

1. List and briefly describe 4 types of processor scheduling policies.
2. Compare Long Term, Medium Term and Short Term scheduling  
3. List 4 desired scheduled algorithm characteristics
4. Describe 2 methods to assign processes to processors in multiprocessing
5. How is parallel computing different from multiprocessing?   ( 1 point)

Given the following cash flows for a proposed capital investment project, calculate the payback period.

Question 4 options:

Problem 4) Five coins are flipped. The first four coins will land on heads with probability 1/4. The fifth coin is a fair coin. Assume that the results of the flips are independent. Let X be the total number of heads that result.

(hint: Condition on the last flip).

a) Find P(X=2)

b) Determine E[X]

Q: A computer consulting firm presently has bids out on three projects. Let A_i = {awarded project i}, for i = 1, 2, 3, and suppose that P(A₁) = 0.23, P(A₂) = 0.25, P(A₃) = 0.29, P(A₁ ∩ A₂) = 0.07, P(A₁ ∩ A₃) = 0.05, P(A₂ ∩ A₃) = 0.08, P(A₁ ∩ A₂ ∩ A₃) = 0.02. Use the probabilities given above to compute the following probabilities, and explain in words the meaning of each one. (Round your answers to four decimal places.)

(a)    P(A₂ | A₁) =

Explain this probability in words.

If the firm is awarded project 2, this is the chance they will also be awarded project 1. If the firm is awarded project 1, this is the chance they will also be awarded project 2.     This is the probability that the firm is awarded either project 1 or project 2. This is the probability that the firm is awarded both project 1 and project 2.

(b)    P(A₂ ∩ A₃ | A₁) =

Explain this probability in words.

This is the probability that the firm is awarded projects 1, 2, and 3. If the firm is awarded project 1, this is the chance they will also be awarded projects 2 and 3.     If the firm is awarded projects 2 and 3, this is the chance they will also be awarded project 1. This is the probability that the firm is awarded at least one of the projects.

(c)    P(A₂ ∪ A₃ | A₁) =

Explain this probability in words.

If the firm is awarded project 1, this is the chance they will also be awarded at least one of the other two projects. This is the probability that the firm is awarded at least one of the projects.     If the firm is awarded at least one of projects 2 and 3, this is the chance they will also be awarded project 1. This is the probability that the firm is awarded projects 1, 2, and 3.

(d)    P(A₁ ∩ A₂ ∩ A₃ | A₁ ∪ A₂ ∪ A₃) =

Explain this probability in words.

This is the probability that the firm is awarded at least one of the projects. This is the probability that the firm is awarded projects 1, 2, and 3.     If the firm is awarded at least two of the projects, this is the chance that they will be awarded all three projects. If the firm is awarded at least one of the projects, this is the chance that they will be awarded all three projects.

Q: Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.38 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar.

(a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.)

(b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.)

Use the cumulative distribution function of X to calculate

P(2 ≤ X ≤ 7).

(Round your answer to four decimal places.)

P(2 ≤ X ≤ 7) =

1.) Metlock Company is constructing a building. Construction began on February 1 and was completed on December 31. Expenditures were $2,520,000 on March 1, $1,680,000 on June 1, and $4,200,000 on December 31.

Metlock Company borrowed $1,400,000 on March 1 on a 5-year, 12% note to help finance construction of the building. In addition, the company had outstanding all year a 12%, 5-year, $2,800,000 note payable and an 11%, 4-year, $4,900,000 note payable. Compute avoidable interest for Metlock Company. Use the weighted-average interest rate for interest capitalization purposes. (Round "Weighted-average interest rate" to 4 decimal places, e.g. 0.2152 and final answer to 0 decimal places, e.g. 5,275.)

Avoidable interest $___________

2.) Marigold Company is constructing a building. Construction began on February 1 and was completed on December 31. Expenditures were $2,052,000 on March 1, $1,200,000 on June 1, and $3,007,200 on December 31.

Marigold Company borrowed $1,042,720 on March 1 on a 5-year, 13% note to help finance construction of the building. In addition, the company had outstanding all year a 9%, 5-year, $2,039,800 note payable and an 10%, 4-year, $3,462,500 note payable. Compute the weighted-average interest rate used for interest capitalization purposes. (Round answer to 2 decimal places, e.g. 7.58%.)

Weighted-average interest rate:____________%

Sorting Benchmarks
Write a program that generates and sorts an array of a user-specified number (arraySize) of randomly generated numbers. To keep the values to a reasonable range by using the array size as the upper bound for the random numbers (between 1 and arraySize). Your program should call the individual functions that implement the five sorting algorithms discussed in class (see the lecture slides). Each function should keep a count of the number of comparisons/exchanges it makes. Display the pre-sorted array, the sorted array, and the number of comparisons for each algorithm.

Note: In this assignment, you will compare all the five sorting algorithms from the lecture notes (brute force sort, bubble sort, bubble sort++, selection sort, and insertion sort) with each other using the same data for each. Start with getting one to work first. The idea is that once you have one, adding in the other algorithms is relatively simple. Hint: use the algorithms from the slides! Your program MUST include a function for each algorithm and use them appropriately. The main procedural code must first prompt the user for the arraySize = number of elements to store in the array ("How many elements in the array?"). Then, it will generate arraySize random integers between 1 and arraySize (the number they entered--yes, you will use it twice!). Since each function will sort the array, changing the values, you will need to make multiple copies of the generated array to test the same numbers against each algorithm. Each algorithm will return the number of comparisons made. This is when one element is compared to another, regardless of whether or not they get swapped. NO GLOBAL VARIABLES!

You will need to include at least these functions:
void displayArray(int values[], int size);
int bruteForceSort(int values[], int size);
int bubbleSort(int values[], int size);
int bubblePPSort(int values[], int size);
int selectionSort(int values[], int size);
int insertionSort(int values[], int size);

The output should look something like this -- user inputs are in bold blue type:
How many elements in the array? 20
BRUTE FORCE SORT
Before sorting:
10 14 6 7 12 18 9 13 4 17 19 2 17 2 4 10 20 3 9 14
After sorting:
2 2 3 4 4 6 7 9 9 10 10 12 13 14 14 17 17 18 19 20
Number of comparisons: 400

BUBBLE SORT
Before sorting:
10 14 6 7 12 18 9 13 4 17 19 2 17 2 4 10 20 3 9 14
After sorting:
2 2 3 4 4 6 7 9 9 10 10 12 13 14 14 17 17 18 19 20
Number of comparisons: 190

BUBBLE SORT PLUS PLUS
Before sorting:
10 14 6 7 12 18 9 13 4 17 19 2 17 2 4 10 20 3 9 14
After sorting:
2 2 3 4 4 6 7 9 9 10 10 12 13 14 14 17 17 18 19 20
Number of comparisons: 184

SELECTION SORT
Before sorting:
10 14 6 7 12 18 9 13 4 17 19 2 17 2 4 10 20 3 9 14
After sorting:
2 2 3 4 4 6 7 9 9 10 10 12 13 14 14 17 17 18 19 20
Number of comparisons: 206

INSERTION SORT
Before sorting:
10 14 6 7 12 18 9 13 4 17 19 2 17 2 4 10 20 3 9 14
After sorting:
2 2 3 4 4 6 7 9 9 10 10 12 13 14 14 17 17 18 19 20
Number of comparisons: 186